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Irs. Sara;, P. '.Valsworth 

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Entered according to Act of Congress, in the year 1840, by 

in the Clerk's Office of the District Court of Massachusetts. 


" IF the present age is distinguished by more clear 
and just views of social and political science, it is not 
less marked by the disposition, so unequivocally and 
universally manifested, to reject the inordinate estimate 
heretofore set upon merely ornamental literature ; and 
whilst it does not refuse their just rank and influence 
to such studies, it admits to that high consideration to 
which they are entitled, the sciences which explain the 
beautiful phenomena of the physical world. 

" The public now demand of those professionally 
devoted to the sciences, that they shall not confine the 
knowledge they have such favored opportunities of ac- 
quiring, to the lecture-room, but shall render it, as far as 
practicable, available to the well-informed of all profes- 
sions, and to the more intelligent, at least, of the other 
sex." Edinburgh Review for April, 1835. 


PREFACE, ...*... ^ 3 

Introductory Observations, >". "\ . 9 

Doctrine of the Sphere, 16 

Astronomical Instruments. Telescope, 29 

Telescope continued, 36 

Observatories, 45t 

Time and the Calendar, . .'.'. 59 


Figure of the Earth, . . . . . ;-T^. f-'\ . 69 


Diurnal Revolution, . /'".'*." '.; ; .v^v ... 81 


Parallax and Refrartion, ! v* 89 



The Sun, 101 

Annual Revolution. Seasons, Ill 

Laws of Motion, 126 

Terrestrial Gravity, 134 


Sir Isaac Newton. Universal Gravitation. Figure 
of the Earth's Orbit. Precession of the Equinoxes, \ 43 

The Moon, 157 


The Moon. Phases. Harvest Moon. Librations, . 172 

Moon's Orbit. Her Irregularities, 180 

Eclipses, 195 


Longitude. Tides, 208 


Planets. Mercury and Venus, 225 

Superior Planets : Mars, Jupiter, Saturn, and Uranus, 243 


Copernicus. Galileo, . . . .... . . . 254 

Saturn. Uranus. Asteroids, . . .... . . 274 

The Planetary Motions. Kepler's Laws. Kepler, . 291 

Comets, 312 

Comets, . .334 

Meteoric Showers, . 346 


Fixed Stars, ."V. . . 365 


Fixed Stars, . . . . . . . / 383 


System of the World, . . . . .; 392 

Conclusion, . .... V 406 

INDEX, ..'; . . 415 




"Ye sacred Muses, -with whose beauty fired, 
My soul is ravished, and my brain inspired, 
Whose priest I am, whose holy fillets wear ; 
Would you your poet's first petition hear, 
Give me the ways of wandering stars to know, 
The depths of heaven above, and earth below ; 
Teach me the various labors of the moon, 
And whence proceed th' eclipses of the sun; 
Why flowing tides prevail upon the main, 
And in what dark recess they shrink again ; 
What shakes the solid earth, what cause delays 
The Summer nights, and shortens Winter days." 

Dryden's Virgil. 

To MRS. C M . 

DEAR MADAM, In the conversation we recently held 
on the study of Astronomy, you expressed a strong 
desire to become better acquainted with this noble sci- 
ence, but said you had always been repelled by the air 
of severity which it exhibits, arrayed as it is in so many 
technical terms, and such abstruse mathematical pro- 
cesses : or, if you had taken up some smaller treatise, 
with the hope of avoiding these perplexities, you had 
always found it so meager and superficial, as to afford 
you very little satisfaction. You asked, if a work might 
not be prepared, which would convey to the general 
reader some clear and adequate knowledge of the great 
discoveries in astronomy, and yet require for its perusal 
no greater preparation, than may be presumed of every 
well-educated English scholar of either sex. 

You were pleased to add the request, that I would 


write such a work, a work which should combine, 
with a luminous exposition of the leading truths of the 
science, some account of the interesting historical facts 
with which it is said the records of astronomical dis- 
covery abound. Having, moreover, heard much of the 
grand discoveries which, within the last fifty years, have 
been made among the fixed stars, you expressed a 
strong desire to learn more respecting these sublime 
researches. Finally, you desired to see the argument 
for the existence and natural attributes of the Deity, as 
furnished by astronomy, more fully and clearly exhibit- 
ed, than is done in any work which you have hitherto 
perused. In the preparation of the proposed treatise, 
you urged me to supply, either in the text or in notes, 
every elementary principle which would be essential 
to a perfect understanding of the work ; for although, 
while at school, you had paid some attention to geom- 
etry and natural philosophy, yet so much time had 
since elapsed, that your memory required to be re- 
freshed on the most simple principles of these elemen- 
tary studies, and you preferred that I should consider 
you as altogether unacquainted with them. 

Although, to satisfy a mind, so cultivated and inquisi- 
tive as yours, may require a greater variety of powers 
and attainments than I possess, yet, as you were pleased 
to urge me to the trial, I have resolved to make the at- 
tempt, and will see how far I may be able to lead you 
into the interior of this beautiful temple, without oblig- 
ing you to force your way through the "jargon of the 

Astronomy, however, is a very difficult or a compar- 
atively easy study, according to the view we take of it. 
The investigation of the great laws which govern the 
motions of the heavenly bodies has commanded the 
highest efforts of the human mind ; but profound truths, 
which it required the mightiest efforts of the intellect to 
disclose, are often, when once discovered, simple in their 
complexion, and may be expressed in very simple terms. 
Thus, the creation of that element, on whose mysteri- 


ous agency depend all the forms of beauty and loveli- 
ness, is enunciated in these few monosyllables, "And 
God said, let there be light, and there was light ;" and 
the doctrine of universal gravitation, which is the key 
that unlocks the mysteries of the universe, is simply 
this, that every portion of matter in the universe tends 
towards every other. The three great laws of motion, 
also, are, when stated, so plain, that they seem hardly 
to assert any thing but what we knew before. That 
all bodies, if at rest, will continue so, as is declared by 
the first law of motion., until some force moves them ; 
or, if in motion, will continue so, until some force stops 
them, appears so much a matter of course, that we can 
at first hardly see any good reason why it should be 
dignified with the title of the first great law of motion ; 
and yet it contains a truth which it required profound 
sagacity to discover and expound. 

It is, therefore, a pleasing consideration to those who 
have not either the leisure or the ability to follow the 
astronomer through the intricate and laborious processes, 
which conducted him to his great discoveries, that they 
may fully avail themselves of the results of this vast toil, 
and easily understand truths which it required ages of 
the severest labor to unfold. The descriptive parts of 
astronomy, or what may be called the natural history 
of the heavens, is still more easily understood than the 
laws of the celestial motions. The revelations of the 
telescope, and the wonders it has disclosed in the 
sun, in the moon, in the planets, and especially in the 
fixed stars, are facts not difficult to be understood, al- 
though they may affect the mind with astonishment. 

The great practical purpose of astronomy to the 
world is, enabling us safely to navigate the ocean. 
There are indeed many other benefits which it confers 
on man ; but this is the most important. If, however, 
you ask, what advantages the study of astronomy 
promises, as a branch of education, I answer, that 
few subjects promise to the mind so much profit and 
entertainment. It is agreed by writers on the human 


mind, that the intellectual powers are enlarged and 
strengthened by the habitual contemplation of great 
objects, while they are contracted and weakened by 
being constantly employed upon little or trifling sub- 
jects. The former elevate, the latter depress, the 
mind, to their own level. Now, every thing in as- 
tronomy is great. The magnitudes, distances, and 
motions, of the heavenly bodies ; the amplitude of the 
firmament itself ; and the magnificence of the orbs with 
which it is lighted, supply exhaustless materials for 
contemplation, and stimulate the mind to its noblest 
efforts. The emotion felt by the astronomer is not that 
sudden excitement or ecstasy, which wears out life, but 
it is a continued glow of exalted feeling, which gives 
the sensation of breathing in a purer atmosphere than 
others enjoy. We should at first imagine, that a study 
which calls upon its votaries for the severest efforts of 
the human intellect, which demands the undivided toil 
of years, and which robs the night of its accustomed 
hours of repose, would abridge the period of life ; but 
it is a singular fact, that distinguished astronomers, as a 
class, have been remarkable for longevity. I know not 
how to account for this fact, unless we suppose that 
the study of astronomy itself has something inherent in 
it, which sustains its votaries by a peculiar aliment. 

It is the privilege of the student of this department 
of Nature, that his cabinet is already collected, and is 
ever before him ; and he is exempted from the toil of 
collecting his materials of study and illustration, by 
traversing land and sea, or by penetrating into the 
depths of the earth. Nor are they in their nature frail 
and perishable. No sooner is the veil of clouds remov- 
ed, that occasionally conceals the firmament by night, 
than his specimens are displayed to view, bright and 
changeless. The renewed pleasure which he feels, at 
every new survey of the constellations, grows into an af- 
fection for objects which have so often ministered to his 
happiness. His imagination aids him in giving them a 
personification, like that which the ancients gave to the 


constellations ; (as is evident from the names which they 
have transmitted to us ;) and he walks abroad, beneath 
the evening canopy, with the conscious satisfaction and 
delight of being in the presence of old friends. This 
emotion becomes stronger when he wanders far from 
home. Other objects of his attachment desert him ; 
the face of society changes ; the earth presents new 
features ; but the same sun illumines the day, the same 
moon adorns the night, and the same bright stars still 
attend him. 

When, moreover, the student of the heavens can 
command the aid of telescopes, of higher and higher 
powers, new acquaintances are made every evening. 
The sight of each new member of the starry train, that 
the telescope successively reveals to him, inspires a pe- 
culiar emotion of pleasure ; and he at length finds him- 
self, whenever he sweeps his telescope over the firma- 
ment, greeted by smiles, unperceived and unknown to 
his fellow-mortals. The same personification is given 
to these objects as to the constellations, and he seems 
to himself, at times, when he has penetrated into the 
remotest depths of ether, to enjoy the high prerogative 
of holding converse with the celestials. 

It is no small encouragement, to one who wishes to 
acquire a knowledge of the heavens, that the subject is 
embarrassed with far less that is technical than most 
other branches of natural history. Having first learned 
a few definitions, and the principal circles into which, 
for convenience, the sphere is divided, and receiving 
the great laws of astronomy on the authority of the 
eminent persons who have investigated them, you will 
find few hard terms, or technical distinctions, to repel 
or perplex you ; and you will, I hope, find that nothing 
but an intelligent mind and fixed attention are requi- 
site for perusing the Letters which I propose to address 
to you. I shall indeed be greatly disappointed, if the 
perusal does not inspire you with some portion of that 
pleasure, which I have described as enjoyed by the as- 
tronomer himself. 

2 L. A. 


The dignity of the study of the heavenly bodies, and 
its suitableness to the most refined and cultivated mind, 
has been recognised in all ages. Virgil celebrates it in 
the beautiful strains with which I have headed this Let- 
ter, and similar sentiments have ever been cherished by 
the greatest minds. 

As, in the course of these Letters, I propose to trace 
an outline of the history of astronomy, from the earliest 
ages to the present time, you may think this the most 
suitable place for introducing it ; but the successive 
discoveries in the science cannot be fully understood 
and appreciated, until after an acquaintance has been 
formed with the science itself. We must therefore 
reserve the details of this subject for a future opportu- 
nity ; but it may be stated, here, that astronomy was 
cultivated the earliest of all the sciences ; that great 
attention was paid to it by several very ancient nations, 
as the Egyptians and Chaldeans, and the people of In- 
dia and China, before it took its rise in Greece. More 
than six hundred years before the Christian era, howev- 
er, it began to be studied in this latter country. Thales 
and Pythagoras were particularly distinguished for their 
devotion to this science ; and the celebrated school of 
Alexandria, in Egypt, which took its rise about three 
hundred years before the Christian era, and flourished 
for several hundred years, numbered among its disciples 
a succession of eminent astronomers, among whom were 
Hipparchus, Eratosthenes, and Ptolemy. The last of 
these composed a great work on astronomy, called the 
c Almagest,' in which is transmitted to us an account of 
all that was known of the science by the Alexandrian 
school. The ' Almagest' was the principal text-book 
in astronomy, for many centuries afterwards, and com- 
paratively few improvements were made until the age 
of Copernicus. Copernicus was born at Thorn, in 
Prussia, in 1473. Previous to his time, the doctrine 
was held, that the earth is at rest in the centre of the 
universe, and that the sun, moon, and stars, revolve 
about it, every day, from east to west ; in short, that 


the apparent motions of the heavenly bodies are the 
same with their real motions. But Copernicus ex- 
pounded what is now known to be the true theory of 
the celestial motions, in which the sun is placed in the 
centre of the solar system, and the earth and all the 
planets are made to revolve around him, from west to 
east, while the apparent diurnal motion of the heavenly 
bodies, from east to west, is explained by the revolution 
of the earth on its axis, in the same time, from west to 
east ; a motion of which we are unconscious, and which 
we erroneously ascribe to external objects, as we imag- 
ine the shore is receding from us, when we are uncon- 
scious of the motion of the ship that carries us from it. 

Although many of the appearances, presented by the 
motions of the heavenly bodies, may be explained on 
the former erroneous hypothesis, yet, like other hypoth- 
eses founded in error, it was continually leading its 
votaries into difficulties, and blinding their minds to 
the perception of truth. They had advanced nearly as 
far as it was practicable to go in the wrong road ; and 
the great and sublime discoveries of modern times are 
owing, in no small degree, to the fact, that, since the 
days of Copernicus, astronomers have been pursuing 
the plain and simple path of truth, instead of threading 
their way through the mazes of error. 

Near the close, of the sixteenth century, Tycho 
Brahe, a native of Sweden, but a resident of Denmark, 
carried astronomical observations (which constitute the 
basis of all that is valuable in astronomy) to a far 
greater degree of perfection than had ever been done 
before. Kepler, a native of Germany, one of the great- 
est geniuses the world has ever seen, was contemporary 
with Tycho Brahe, and was associated with him in a 
part of his labors. Galileo, an Italian astronomer of 
great eminence, flourished only a little later than Tycho 
Brahe. He invented the telescope, and, both by his 
discoveries and reasonings, contributed greatly to estab- 
lish the true system of the world. Soon after the com- 
mencement of the seventeenth century, (1620,) Lord 


Bacon, a celebrated English philosopher, pointed out 
the true method of conducting all inquiries into the 
phenomena of Nature, and introduced the inductive 
method of philosophizing. According to the inductive 
method, we are to begin our inquiries into the causes 
of any events by first examining and classifying all the 
facts that relate to it, and, from the comparison of these, 
to deduce our conclusions. 

But the greatest single discovery, that has ever been 
made in astronomy, was the law of universal gravitation, 
a discovery made by Sir Isaac Newton, in the latter 
part of the seventeenth century. The discovery of this 
law made us acquainted with the hidden forces that 
move the great machinery of the universe. It furnished 
the key which unlocks the inner temple of Nature ; and 
from this time we may regard astronomy as fixed on a 
sure and immovable basis. I shall hereafter endeavor 
to explain to you the leading principles of universal 
gravitation, when we come to the proper place for in- 
quiring into the causes of the celestial motions, as ex- 
emplified in the motion of the earth around the sun. 



" All are but parts of one stupendous whole, 
Whose body Nature is, and God the soul." Pope. 

LET us now consider what astronomy is, and into 
what great divisions it is distributed ; and then we will 
take a cursory view of the doctrine of the sphere. This 
subject will probably be less interesting to you than 
many that are to follow ; but still, permit me to urge 
upon you the necessity of studying it with attention, 
and reflecting upon each definition, until you fully un- 
derstand it ; for, unless you fully and clearly compre- 
hend the circles of the sphere, and the use that is made 


of them in astronomy, a mist will hang over every sub- 
sequent portion of the science. I beg you, therefore, to 
pause upon every paragraph of this Letter ; and if there 
is any point in the whole which you cannot clearly un- 
derstand, I would advise you to mark it, and to recur 
to it repeatedly ; and, if you finally cannot obtain a clear 
idea of it yourself, I would recommend to you to apply 
for aid to some of your friends, who may be able to as- 
sist you. 

Astronomy is that science which treats of the heav- 
enly bodies. More particularly, its object is to teach 
what is known respecting the sun, moon, planets, com- 
ets, and fixed stars ; and also to explain the methods by 
which this knowledge is acquired. Astronomy is some- 
times divided into descriptive, physical, and practical. 
Descriptive astronomy respects facts; physical astrono- 
my, causes ; practical astronomy, the means of investi- 
gating the facts, whether by instruments or by calcu- 
lation. It is the province of descriptive astronomy to 
observe, classify, and record, all the phenomena of the 
heavenly bodies, whether pertaining to those bodies in- 
dividually, or resulting from their motions and mutual 
relations. It is the part of physical astronomy to ex- 
plain the causes of these phenomena, by investigating 
the general laws on which they depend ; especially, by 
tracing out all the consequences of the law of universal 
gravitation. Practical astronomy lends its aid to both 
the other departments. 

The definitions of the different lines, points, and 
circles, which are used in astronomy, and the proposi- 
tions founded upon them, compose the doctrine of the 
sphere. Before these definitions are given, I must re- 
call to your recollection a few particulars respecting the 
method of measuring angles. (See Fig. 1, page 18.) 

A line drawn from the centre to the circumference 
of a circle is called a radius, as C D, C B, or C K. 

Any part of the circumference of a circle is called an 
arc, as A B, or B D. 

An angle is measured by an arc included between 



two radii. Thus, in Fig. 
1, the angle contained be- 
tween the two radii, C A 
and C B, that is, the angle 
A C B, is measured by the 
arc A B. Every circle, it 
will be recollected, is divi- 
ded into three hundred and 
sixty equal parts, called de- 
grees ; and any arc, as A B, 
contains a certain number 
of degrees, according to 
its length. Thus, if the arc A B contains forty de- 
grees, then the opposite angle A C B is said to be an 
angle of forty degrees, and to be measured by A B. 
But this arc is the same part of the smaller circle that 
E F is of the greater. The arc A B, therefore, con- 
tains the same number of degrees as the arc E F, and 
either may be taken as the measure of the angle A C B. 
As the whole circle contains three hundred and sixty de- 
grees, it is evident, that the quarter of a circle, or quad- 
rant, contains ninety degrees, and that the semicircle 
A B D G contains one hundred and eighty degrees. 

The complement of an arc, or angle, is what it wants 
of ninety degrees. Thus, since A D is an arc of nine- 
ty degrees, B D is the complement of A B, and A B is 
the complement of B D. If A B denotes a certain 
number of degrees of latitude, B D will be the comple- 
ment of the latitude, or the colatitude, as it is commonly 

The supplement of an arc, or angle, is what it wants 
of one hundred and eighty degrees. Thus, B A is the 
supplement of G D B, and G D B is the supplement of 
B A. If B A were twenty degrees of longitude, G D B, 
its supplement, would be one hundred and sixty de- 
grees. An angle is said to be subtended by the side 
which is opposite to it. Thus, in the triangle A C K, 
the angle at C is subtended by the side A K, the angle 
at A by C K, and the angle at K by C A. In like man- 


ner, a side is said to be subtended by an angle, as A K 
by the angle at C. 

Let us now proceed with the doctrine of the sphere. 

A section of a sphere, by a plane cutting it in any 
manner, is a circle. Great circles are those which pass 
through the centre of the sphere, and divide it into. two 
equal hemispheres. Small circles are such as do not 
pass through the centre, but divide the sphere into two 
unequal parts. The axis of a circle is a straight line 
passing through its centre at right angles to its plane. 
The pole of a great circle is the point on the sphere 
where its axis cuts through the sphere. Every great 
circle has two poles, each of which is every where nine- 
ty degrees from the great circle. All great circles of 
the sphere cut each other in two points diametrically 
opposite, and consequently their points of section are 
one hundred and eighty degrees apart. A great circle, 
which passes through the pole of another great circle, 
cuts the latter at right angles. The great circle which 
passes through the pole of another great circle, and is 
at right angles to it, is called a secondary to that 
circle. The angle made by two great circles on the 
surface of the sphere is measured by an arc of an- 
other great circle, of which the angular point is the 
pole, being the arc of that great circle intercepted be- 
tween those two circles. 

In order to fix the position of any place, either on 
the surface of the earth or in the heavens, both the 
earth and the heavens are conceived to be divided into 
separate portions, by circles, which are imagined to cut 
through them, in various ways. The earth thus inter- 
sected is called the terrestrial, and the heavens the ce- 
lestial, sphere. We must bear in mind, that these cir- 
cles have no existence in Nature, but are mere land- 
marks, artificially contrived for convenience of refer- 
ence. On account of the immense distances of the 
heavenly bodies, they appear to us, wherever we are 
placed, to be fixed in the same concave surface, or ce- 
lestial vault. The great circles of the globe, extended 


every way to meet the concave sphere of the heavens, 
become circles of the celestial sphere. 

The horizon is the great circle which divides the 
earth into upper and lower hemispheres, and separates 
the visible heavens from the invisible. This is the ra- 
tional horizon. The sensible horizon is a circle touch- 
ing the earth at the place of the spectator, and is bound- 
ed by the line in which the earth and skies seem to 
meet. The sensible horizon is parallel to the rational, 
but is distant from it by the semidiameter of the earth, 
or nearly four thousand miles. Still, so vast is the dis- 
tance of the starry sphere, that both these planes ap- 
pear to cut the sphere in the same line ; so that we see 
the same hemisphere of stars that we should see, if the 
upper half of the earth were removed, and we stood on 
the rational horizon. 

The poles of the horizon are the zenith and nadir. 
The zenith is the point directly over our heads ; and 
the nadir, that directly under our feet. The plumb- 
line (such as is formed by suspending a bullet by a 
string) is in the axis of the horizon, and consequently 
directed towards its poles. Every place on the surface 
of the earth has its own horizon ; and the traveller has 
a new horizon at every step, always extending ninety 
degrees from him, in all directions. 

Vertical circles are those which pass through the poles 
of the horizon, (the zenith and nadir,) perpendicular to it. 

The meridian is that vertical circle which passes 
through the north and south points. 

The prime vertical is that vertical circle which,pas- 
ses through the east and west points. 

The altitude of a body is its elevation above the ho- 
rizon, measured on a vertical circle. 

The azimuth of a body is its distance, measured on 
the horizon, from the meridian to a vertical circle pass- 
ing through that body. 

The amplitude of a body is its distance, on the ho- 
rizon, from the prime vertical to a vertical circle pass- 
ing through the body. 


Azimuth is reckoned ninety degrees from either the 
north or south point ; and amplitude ninety degrees 
from either the east or west point. Azimuth and am- 
plitude are mutually complements of each other, for 
one makes up what the other wants of ninety degrees. 
When a point is on the horizon, it is only necessary 
to count the number of degrees of the horizon between 
that point and the meridian, in order to find its azi- 
muth ; but if the point is above the horizon, then its 
azimuth is estimated by passing a vertical circle through 
it, and reckoning the azimuth from the point where 
this circle cuts the horizon. 

The zenith distance of a body is measured on a ver- 
tical circle passing through that body. It is the com- 
plement of the altitude. 

The axis of the earth is the diameter on which the 
earth is conceived to turn in its diurnal revolution. 
The same line, continued until it meets the starry con- 
cave, constitutes the axis of the celestial sphere. 

The poles of the earth are the extremities of the 
earth's axis : the poles of the heavens, the extremities 
of the celestial axis. 

The equator is a great circle cutting the axis of the 
earth at right angles. Hence, the axis of the earth is 
the axis of the equator, and its poles are the poles of 
the equator. The intersection of the plane of the equa- 
tor with the surface of the earth constitutes the terres- 
trial, and its intersection with the concave sphere of 
the heavens, the celestial., equator. The latter, by way 
of distinction, is sometimes denominated the equinoctial. 

T?te secondaries to the equator, that is, the great 
circles passing through the poles of the equator, are 
called meridians, because that secondary which passes 
through the zenith of any place is the meridian of that 
place, and is at right angles both to the equator and 
the horizon, passing, as it does, through the poles of 
both. These secondaries are also called hour circles^ 
because the arcs of the equator intercepted between 
them are used as measures of time. 


The latitude of a place on the earth is its distance 
from the equator north or south. The polar distance, 
or angular distance from the nearest pole, is the com- 
plement of the latitude. 

The longitude of a place is its distance from some 
standard meridian, either east or west, measured on the 
equator. The meridian, usually taken as the standard, 
is that of the Observatory of Greenwich, in London. 
If a place is directly on the equator, we have only to 
inquire, how many degrees of the equator there are be- 
tween that place and the point where the meridian of 
Greenwich cuts the equator. If the place is north or 
south of the equator, then its longitude is the arc of the 
equator intercepted between the meridian which passes 
through the place and the meridian of Greenwich. 

The ecliptic is a great circle, in which the earth 
performs its annual revolutions around the sun. It 
passes through the centre of the earth and the centre 
of the sun. It is found, by observation, that the earth 
does not lie with its axis at right angles to the plane of 
the ecliptic, so as to make the equator coincide with it. 
but that it is turned about twenty-three and a half de- 
grees out of a perpendicular direction, making an angle 
with the plane itself of sixty-six and a half degrees. 
The equator, therefore, must be turned the same dis- 
tance out of a coincidence with the ecliptic, the two 
circles making an angle with each other of twenty- 
three and a half degrees. It is particularly important 
that we should form correct ideas of the ecliptic, and 
of its relations t . the equator, since to these two cir- 
cles a great number of astronomical measurements and 
phenomena are referred. 

The equinoctial points, or equinoxes, are the inter- 
sections of the ecliptic and equator. The time when 
the sun crosses the equator, in going northward, is call- 
ed the vernal, and in returning southward, the autum- 
nal, equinox. The vernal equinox occurs about the 
twenty-first of March, and the autumnal, about the 
twenty-second of September. 


The solstitial points are the two points of the eclip- 
tic most distant from the equator. The times when 
the sun comes to them are called solstices. The Sum- 
mer solstice occurs about the twenty-second of June, 
and the Winter solstice about the twenty-second of 
December. The ecliptic is divided into twelve equal 
parts, of thirty degrees each, called signs, which, be- 
ginning at the vernal equinox, succeed each other, in 
the following order : 

1. Aries, f 7. Libra, =s= 

2. Taurus, y 8. Scorpio, TH. 

3. Gemini, n 9. Sagittarius, / 

4. Cancer, Z5 10. Capricornus, vj 

5. Leo, SI 11. Aquarius, *# 

6. Virgo, TIK 12. Pisces. X 
The mode of reckoning on the ecliptic is by signs, 

degrees, minutes, and seconds. The sign is denoted 
either by its name or its number. Thus, one hundred 
degrees may be expressed either as the tenth degree of 
Cancer, or as 3s 10. It will be found an advantage 
to repeat the signs in their proper order, until they are 
well fixed in the memory, and to be able to recognise 
each sign by its appropriate character. 

Of the various meridians, two are distinguished by 
the name of colures. The equinoctial colure is the 
meridian which passes through the equinoctial points. 
From this meridian, right ascension and celestial longi- 
tude are reckoned, as longitude on the earth is reckon- 
ed from the meridian of Greenwich. The solstitial 
colure is the meridian which passes through the sol- 
stitial points. 

The position of a celestial body is referred to the 
equator by its right ascension and declination. Right 
ascension is the angular distance from the vernal equi- 
nox measured on the equator. If a star is situated on 
the equator, then its right ascension is the number of 
degrees of the equator between the star and the vernal 
equinox. But if the star is north or south of the equa- 
tor, then its right ascension is the number of degrees of 


the equator, intercepted between the vernal equinox 
and that secondary to the equator which passes through 
the star. Declination is the distance of a body from 
the equator measured on a secondary to the latter. 
Therefore, right ascension and declination correspond 
to terrestrial longitude and latitude, right ascension 
being reckoned from the equinoctial colure, in the same 
manner as longitude is reckoned from the meridian of 
Greenwich. On the other hand, celestial longitude 
and latitude are referred, not to the equator, but to the 
ecliptic. Celestial longitude is the distance of a body 
from the vernal equinox measured on the ecliptic. Ce- 
lestial latitude is the distance from the ecliptic meas- 
ured on a secondary to the latter. Or, more briefly, 
longitude is distance on the ecliptic : latitude, distance 
from the ecliptic. The north polar distance of a star 
is the complement of its declination. 

Parallels of latitude are small circles parallel to the 
equator. They constantly diminish in size, as we go 
from the equator to the pole. The tropics are the par- 
allels of latitude which pass through the solstices. The 
northern tropic is called the tropic of Cancer ; the south- 
ern, the tropic of Capricorn. The polar circles are the 
parallels of latitude that pass through the poles of the 
ecliptic, at the distance of twenty-three and a half de- 
grees from the poles of the earth. 

The elevation of the pole of the heavens above the 
horizon of any place is always equal to the latitude of 
the place. Thus, in forty degrees of north latitude we 
see the north star forty degrees above the northern ho- 
rizon ; whereas, if we should travel southward, its ele- 
vation would grow less and less, until we reached the 
equator, where it would appear in the horizon. Or, if 
we should travel northwards, the north star would rise 
continually higher and higher, until, if we could reach 
the pole of the earth, that star would appear directly 
over head. The elevation of the equator above the 
horizon of any place is equal to the complement of 
the latitude. Thus, at the latitude of forty degrees 


north, the equator is elevated fifty degrees above the 
southern horizon. 

The earth is divided into five zones. That portion 
of the earth which lies between the tropics is called 
the torrid zone ; that between the tropics and the po- 
lar circles, the temperate zones ; and that between the 
polar circles and the poles, the frigid zones. 

The zodiac is the part of the celestial sphere which 
lies about eight degrees on each side of the eclip- 
tic. This portion of the heavens is thus marked off by 
itself, because all the planets move within it. 

After endeavoring to form, from the definitions, as 
clear an idea as we can of the various circles of the 
sphere, we may next resort to an artificial globe, and 
see how they are severally represented there. I do not 
advise to begin learning the definitions from the globe ; 
the mind is more improved, and a power of conceiving 
clearly how things are in Nature is more effectually ac- 
quired, by referring every thing, at first, to the grand 
sphere of Nature itself, and afterwards resorting to ar- 
tificial representations to aid our conceptions. We can 
get but a very imperfect idea of a man from a profile 
cut in paper, unless we know the original. If we are 
acquainted with the individual, the profile will assist us 
to recall his appearance more distinctly than we can do 
without it. In like manner, orreries, globes, and other 
artificial *aids, will be found very useful, in assisting us 
to form distinct conceptions of the relations existing be- 
tween the different circles of the sphere, and of the 
arrangements of the heavenly bodies ; but, unless we 
have already acquired some correct ideas of these 
things, by contemplating them as they are in Nature, 
artificial globes, and especially orreries, will be apt to 
mislead us. 

I trust you will be able to obtain the use of a globe,* 

* A small pair of globes, that will answer every purpose required 
by the readers of these Letters, may be had of the publishers of this 
Work, at a price not exceeding ten dollars ; or half that sum for a 
celestial globe, which will serve alone for studying astronomy. 
3 L. A. 



to aid you in the study of the foregoing definitions, or 
doctrine of the sphere ; but if not, I would recommend 
the following easy device. To represent the earth, 
select a large apple, (a melon, when in season, will be 
found still better.) The eye and the stem of the ap- 
ple will indicate the position of the two poles of the 
earth. Applying the thumb and finger of the left hand 
to the poles, and holding the apple so that the poles 
may be in a north and south line, turn this globe from 
west to east, and its motion will correspond to the di- 
urnal movement of the earth. Pass a wire or a knit- 
ting needle through the poles, and it will represent the 
axis of the sphere. A circle cut around the apple, half 
way between the poles, will be the equator ; and sev- 
eral other circles cut between the equator and the poles, 
parallel to the equator, will represent parallels of lati- 
tude ; of which, two, drawn twenty-three and a half de- 
grees from the equator, will be the tropics, and two 
others, at the same distance from the poles, will be the 
polar circles. A great circle cut through the poles, in 
a north and south direction, will form the meridian, 
and several other great circles drawn through the poles, 
and of course perpendicularly to the equator, will be 
secondaries to the equator, constituting meridians, or 
hour circles. A great circle cut through the centre of 
the earth, from one tropic to the other, would represent 
the plane of the ecliptic ; and consequently a line cut 
round the apple where such a section meets the sur- 
face, will be the terrestrial ecliptic. The points where 
this circle meets the tropics indicate the position of the 
solstices ; and its intersection with the equator, that of 
the equinoctial points. 

The horizon is best represented by a circular piece 
of pasteboard, cut so as to fit closely to the apple, be- 
ing movable upon it. When this horizon is passed 
through the poles, it becomes the horizon of the equa- 
tor ; when it is so placed as to coincide with the earth's 
equator, it becomes the horizon of the poles ; and in 
every other situation it represents the horizon of a 


place on the globe ninety degrees every way from it. 
Suppose we are in latitude forty degrees ; then let us 
place our movable paper parallel to our own horizon, 
and elevate the pole forty degrees above it, as near as 
we can judge by the eye. If we cut a circle around 
the apple, passing through its highest part, and through 
the east and west points, it will represent the prime 

Simple as the foregoing device is, if you will take 
the trouble to construct one for yourself, it will lead 
you to more correct views of the doctrine of the sphere, 
than you would be apt to obtain from the most expen- 
sive artificial globes, although there are many other use- 
ful purposes which such globes serve, for which the ap- 
ple would be inadequate. When you have thus made 
a sphere for yourself, or, with an artificial globe before 
you, if you have access to one, proceed to point out on 
it the various arcs of azimuth and altitude, right ascen- 
sion and declination, terrestrial and celestial latitude 
and longitude, these last being referred to the equa- 
tor on the earth, and to the ecliptic in the heavens. 

When the circles of the sphere are well learned, we 
may advantageously employ projections of them in va- 
rious illustrations. By the projection of the sphere is 
meant a representation of all its parts on a plane. The 
plane itself is called the plane of projection. Let us 
take any circular ring, as a wire bent into a circle, and 
hold it in different positions before the eye. If we hold 
it parallel to the face, with the whole breadth opposite 
to the eye, we see it as an entire circle. If we turn it 
a little sideways, it appears oval, or as an ellipse ; and, 
as we continue to turn it more and more round, the 
ellipse grows narrower and narrower, until, when the 
edge is presented to the eye, we see nothing but a line. 
Now imagine the ring to be near a perpendicular wall, 
and the eye to be removed at such a distance from it, 
as not to distinguish any interval between the ring and 
the wall ; then the several figures under which the ring 
is seen will appear to be inscribed on the wall, and we 


shall see the ring as a circle, when perpendicular to a 
straight line joining the centre of the ring and the eye, 
or as an ellipse, when oblique to this line, or as a straight 
line, when its edge is towards us. 

It is in this manner that the circles of the sphere are 
projected, as represented in the following diagram, Fig. 2. 

Here, various circles 
are represented as 
projected on the me- 
ridian, which is sup- 
posed to be situated 
directly before the 
eye, at some distance 
from it. The horizon 
H O, being perpendic- 
ular to the meridian, 
is seen edgewise^ and 
consequently is pro- 
jected into a straight 
line. The same is the 
case with the prime vertical Z N, with the equator E Q, 
and the several small circles parallel to the equator, 
which represent the two tropics and the two polar cir- 
cles. In fact, all circles whatsoever, which are perpen- 
dicular to the plane of projection, will be represented 
by straight lines. But every circle which is perpen- 
dicular to the horizon, except the prime vertical, being 
seen obliquely, as Z M N, will be projected into an 
ellipse, one half only of which is seen, the other half 
being on the other side of the plane of projection. In 
the same manner, P R P, an hour circle, is represented 
by an ellipse on the plane of projection. 




" Here truths sublime, and sacred science charm, 
Creative arts new faculties supply, 
Mechanic powers give more than giant's arm, 
And piercing optics more than eagle's eye; 
Eyes that explore creation's wondrous laws, 
And teach us to adore the great Designing Cause." Beattie. 

IF, as I trust, you have gained a clear and familiar 
knowledge of the circles and divisions of the sphere, 
and of the mode of estimating the position of a heav- 
enly body by its azimuth and altitude, or by its right as- 
cension and declination, or by its longitude and latitude, 
you will now enter with advantage upon an account 
of those instruments, by means of which our knowl- 
edge of astronomy has been greatly promoted and per- 

The most ancient astronomers employed no instru- 
ments of observation, but acquired their knowledge of 
the heavenly bodies by long-continued and most atten- 
tive inspection with the naked eye. Instruments for 
measuring angles were first used in the Alexandrian 
school, about three hundred years before the Christian 

Wherever we are situated on the earth, we appear to 
be in the centre of a vast sphere, on the concave sur- 
face of which all celestial objects are inscribed. If we 
take any two points on the surface of the sphere, as two 
stars, for example, and imagine straight lines to be 
drawn to them from the eye, the angle included be- 
tween these lines will be measured by the arc of the 
sky contained between the two points. Thus, if D B H, 
Fig. 3, page 30, represents the concave surface of the 
sphere, A, B, two points on it, as two stars, and C A, 
C B, straight lines drawn from the spectator to those 
points, then the angular distance between them is meas- 
ured by the arc A B, or the angle A C B. But this an* 


Fig. 3. 

gle may be measured on a much smaller circle, having 
the same centre, as G F K, since the arc E F will have 
the same number of degrees as the arc A B. The sim- 
plest mode of taking an angle between two stars is by 
means of an arm opening at a joint like the blade of a 
penknife, the end of the arm moving like C E upon the 
graduated circle K F G. In fact, an instrument con- 
structed on this principle, resembling a carpenter's rule 
with a folding joint, with a semicircle attached, consti- 
tuted the first rude apparatus for measuring the angular 
distance between two points on the celestial sphere. 
Thus the sun's elevation above the horizon might be 
ascertained, by placing one arm of the rule on a level 
with the horizon, and bringing the edge of the other in- 
to a line with the sun's centre. 

The common surveyor's compass affords a simple 
example of angular measurement. Here, the needle 
lies in a north and south line, while the circular rim of 
the compass, when the instrument is level, corresponds 
to the horizon. Hence the compass shows the azimuth 
of an object, or how many degrees it lies east or west 
of the meridian. 

It is obvious, that the larger the graduated circle is, 
the more minutely its limb may be divided. If the cir- 
cle is one foot in diameter, each degree will occupy one 
tenth of an inch. If the circle is twenty feet in diame- 
ter, a degree will occupy the space of two inches, and 
could be easily divided into minutes, since each minute 
would cover a space one thirtieth of an inch. Refined 


astronomical circles are now divided with very great 
skill and accuracy, the spaces between the divisions be- 
ing, when read off, magnified by a microscope ; but in 
former times, astronomers had no mode of measuring 
small angles but by employing very large circles. But the 
telescope and microscope enable us at present to meas- 
ure celestial arcs much more accurately than was done 
by the older astronomers. In the best instruments, the 
measurements extend to a single second of space, or 
one thirty-six hundredth part of a degree, a space, on a 
circle twelve feet in diameter, no greater than one fifty- 
seven hundredth part of an inch. To divide, or gradu- 
ate, astronomical instruments, to such a degree of nicety, 
requires the highest efforts of mechanical skill. Indeed, 
the whole art of instrument-making is regarded as the 
most difficult and refined of all the mechanical arts ; 
and a few eminent artists, who have produced instru- 
ments of peculiar power and accuracy, take rank with 
astronomers of the highest celebrity. 

I will endeavor to make you acquainted with several 
of the principal instruments employed in astronomical 
observations, but especially with the telescope, which is 
the most important and interesting of them all. I think 
I shall consult your wishes, as well as your improve- 
ment, by giving you a clear insight into the principles 
of this prince of instruments, and by reciting a few par- 
ticulars, at least, respecting its invention and subsequent 

The Telescope, as its name implies, is an instrument 
employed for viewing distant objects.* It aids the eye 
in two ways ; first, by enlarging the visual angle under 
which objects are seen, and, secondly, by collecting and 
conveying to the eye a much larger amount of the light 
that emanates from the object, than would enter the 
naked pupil. A complete knowledge of the telescope 
cannot be acquired, without an acquaintance with the 
science of optics ; but one unacquainted with that sci- 

* From two Greek words, ri^e, (tele,) far, and oxonsm, (skopeo,) 
to see. 


ence may obtain some idea of the leading principles of 
this noble instrument. Its main principle is as follows : 
By means of the telescope, we first form an image of 
a distant object, as the moon, for example, and 
then magnify that image by a microscope. 

Let us first see how the image is formed. This may 
be done either by a convex lens, or by a concave mir- 
ror. A convex lens is a flat piece of glass, having its 
two faces convex, or spherical, as is seen in a common 
sun-glass, or a pair of spectacles. Every one who has 
seen a sun-glass, knows, that, when held towards the 
sun, it collects the solar rays into a small bright circle 
in the focus. This is in fact a small image of the sun. 
In the same manner, the image of any distant object, as 
a star, may be formed, as is represented in the following 
diagram. Let A B C D, Fig. 4, represent the tube of 

Fig. 4. 

the telescope. At the front end, or at the end which 
is directed towards the object, (which we will suppose 
to be the moon,) is inserted a convex lens, L, which 
receives the rays of light from the moon, and collects 
them into the focus at a, forming an image of the moon. 
This image is viewed by a magnifier attached to the 
end B C. The lens, L, is called the object-glass, and 
the microscope in B C, the eyeglass. We apply a mi- 
croscope to this image just as we would to any object ; 
and, by greatly enlarging its dimensions, we may render 
its various parts far more distinct than they would oth- 
erwise be ; while, at the same time, the lens collects 
and conveys to the eye a much greater quantity of light 


than would proceed directly from the body under ex- 
amination. A very few rays of light only, from a dis- 
tant object, as a star, can enter the eye directly ; but a 
lens one foot in diameter will collect a beam of light of 
the same dimensions, and convey it to the eye. By 
these means, many obscure celestial objects become 
distinctly visible, which would otherwise be either too 
minute, or not sufficiently luminous, to be seen by us. 

But the image may also be formed by means of a 
concave mirror, which, as well as the concave lens, has 
the property of collecting the rays of light which pro- 
ceed from any luminous body, and of forming an image 
of that body. The image formed by a concave mirror 
is magnified by a microscope, in the same manner as 
when formed by the concave lens. When the lens is 
used to form an image, the instrument is called a re- 
fracting telescope ; when a concave mirror is used, it 
is called a reflecting telescope. 

The office of the object-glass is simply to collect th^ 
light, and to form an image of the object, but not to 
magnify it : the magnifying power is wholly in the eye- 
glass. Hence the principle of the telescope is as fol- 
lows : By means of the object-glass, (in the refracting 
telescope,) or by the concave mirror, (in the reflecting 
telescope,) we form an image of the object, and mag- 
nify that image by a microscope. 

The invention of this noble instrument is generally 
ascribed to the great philosopher of Florence, Galileo. 
He had heard that a spectacle maker of Holland had 
accidentally hit upon a discovery, by which distant ob- 
jects might be brought apparently nearer ; and, without 
further information, he pursued the inquiry, in order to 
ascertain what forms and combinations of glasses would 
produce such a result. By a very philosophical process 
of reasoning, he was led to the discovery of that pecu- 
liar form of the telescope which bears his name. 

Although the telescopes made by Galileo were no 
larger than a common spy-glass of the kind now used 
on board of ships, yet, as they gave new views of the 


heavenly bodies, revealing the mountains and valleys 
of the moon, the satellites of Jupiter, and multitudes of 
stars which are invisible to the naked eye, it was re- 
garded with infinite delight and astonishment. 

Reflecting telescopes were first constructed by Sir 
Isaac Newton, although the use of a concave reflector, 
instead of an object-glass, to form the image, had been 
previously suggested by Gregory, an eminent Scotch as- 
tronomer. The first telescope made by Newton was only 
six inches long. Its reflector, too, was only a little more 
than an inch. Notwithstanding its small dimensions, 
it performed so well, as to encourage further efforts ; 
and this illustrious philosopher afterwards constructed 
much larger instruments, one of which, made with his 
own hands, was presented to the Royal Society of Lon- 
don, and is now carefully preserved in their library. 

Newton was induced to undertake the construction 
of reflecting telescopes, from the belief that refracting 
telescopes were necessarily limited to a very small size, 
with only moderate illuminating powers, whereas the 
dimensions and powers of the former admitted of being 
indefinitely increased. Considerable magnifying pow- 
ers might, indeed, be obtained from refractors, by mak- 
ing them very long ; but the brightness with which 
telescopic objects are seen, depends greatly on the 
dimensions of the beam of light which is collected by 
the object-glass, or by the mirror, and conveyed to the 
eye ; asd therefore, small object-glasses cannot have a 
very high illuminating power. Now, the experiments 
of Newton on colors led him to believe, that it would be 
impossible to employ large lenses in the construction of 
telescopes, since such glasses would give to the images, 
they formed, the colors of the rainbow. But later opti- 
cians have found means of correcting these imperfec- 
tions, so that we are now able to use object-glasses a foot 
or more in diameter, which give very clear and bright 
images. Such instruments are called achromatic tele- 
scopes, a name implying the absence of prismatic or 
rainbow colors in the image. ' It is, however, far more 


difficult to construct large achromatic than large reflect- 
ing telescopes. Very large pieces of glass can seldom 
be found, that are sufficiently pure for the purpose ; 
since every inequality in the glass, such as waves, tears, 
threads, and the like, spoils it for optical purposes, as 
it distorts the light, and produces nothing but confused 

The achromatic telescope (that is, the refracting tel- 
escope, having such an object-glass as to give a colorless 
image) was invented by Dollond, a distinguished Eng- 
lish artist, about the year 1757. He had in his posses- 
sion a quantity of glass of a remarkably fine quality, 
which enabled him to carry his invention at once to a 
high degree of perfection. It has ever since been, with 
the manufacturers of telescopes, a matter of the greatest 
difficulty to find pieces of glass, of a suitable quality for 
object-glasses, more than two or three inches in di- 
ameter. Hence, large achromatic telescopes are very 
expensive, being valued in proportion to the cubes of 
their diameters ; that is, if a telescope whose aperture 
(as the breadth of the object-glass is technically called) 
is two inches, cost one hundred dollars, one whose aper- 
ture is eight inches would cost six thousand four hun- 
dred dollars. 

Since it is so much easier to make large reflecting 
than large refracting telescopes, you may ask, why the 
latter are ever attempted, and why reflectors are not 
exclusively employed ? I answer, that the achromatic 
telescope, when large and well constructed, is a more 
perfect and more durable instrument than the reflecting 
telescope. Much more of the light that falls on the 
mirror is absorbed than is lost in passing through the 
object-glass of a refractor ; and hence the larger achro- 
matic telescopes afford a stronger light than the reflect- 
ing, unless the latter are made of an enormous and un- 
wieldy size. Moreover, the mirror is very liable to 
tarnish, and will never retain its full lustre for many 
years together ; and it is no easy matter to restore the 
lustre, when once impaired. 


In my next Letter, I will give you an account of 
some of the most celebrated telescopes that have ever 
been constructed, and point out the method of using 
this excellent instrument, so as to obtain with it the 
finest views of the heavenly bodies. 



the broad circumference 

Hung on his shoulders like the moon, whose orb 

Through optic glass the Tuscan artist views 

At evening, from the top of Fesole' 

Or in Valdarno, to descry new lands, 

Rivers or mountains, in her spotted globe." Milton. 

, THE two most celebrated telescopes, hitherto made, 
are HerscheYs forty-feet reflector, and the great Dorpat 
refractor. Herschel was a Hanoverian by birth, but 
settled in England in the younger part of his life. 
As early as 1774, he began to make telescopes for his 
own use ; and, during his life, he made more than four 
hundred, of various sizes and powers. Under the pat- 
ronage of George the Third, he completed, in 1789, his 
great telescope, having a tube of iron, forty feet long, 
and a speculum, forty-nine and a half inches or more 
than four feet in diameter. Let us endeavor to form a 
just conception of this gigantic instrument, which we 
can do only by dwelling on its dimensions, and compar- 
ing them with those of other objects with which we are 
familiar, as the length or height of a house, and the 
breadth of a hogshead or cistern, of known dimensions. 
The reflector alone weighed nearly a ton. So large 
and ponderous an instrument must require a vast deal 
of machinery to work it, and to keep it steady ; and, 
accordingly, the frame-work surrounding it was formed 
of heavy timbers, and resembled the frame of a large 
building. When one of the largest of the fixed stars, as 
Sirius, is entering the field of this telescope, its approach 


is announced by a bright dawn, like that which pre- 
cedes the rising sun ; and when the star itself enters the 
field, the light is insupportable to the naked eye. The 
planets are expanded into brilliant luminaries, like the 
moon ; and innumerable multitudes of stars are scat- 
tered like glittering dust over the celestial vault. 

The great Dorpat telescope is of more recent con- 
struction. It was made by Fraunhofer, a German op- 
tician of the greatest eminence, at Munich, in Bavaria, 
and takes its name from its being attached to the ob- 
servatory at Dorpat, in Russia. It is of much smaller 
dimensions than the great telescope of Herschel. Its 
object-glass is nine and a half inches in diameter, and 
its length, fourteen feet. Although the price of this in- 
strument was nearly five thousand dollars, yet it is said 
that this sum barely covered the actual expenses. It 
weighs five thousand pounds, and yet is turned with the 
finger. In facility of management, it has greatly the 
advantage of Herschel's telescope. Moreover, the sky 
of England is so much of the time unfavorable for as- 
tronomical observation, that one hundred good hours 
(or those in which the higher powers can be used) are 
all that can be obtained in a whole year. On this ac- 
count, and on account of the difficulty of shifting the 
position of the instrument, Herschel estimated that it 
would take about six hundred years to obtain with it 
even a momentary glimpse of every part of the heavens. 
This remark shows that such great telescopes are un- 
suited to the common purposes of astronomical observa- 
tion. Indeed, most of Herschel's discoveries were 
made with his small telescopes ; and although, for cer- 
tain rare purposes, powers were applied which magni- 
fied seven thousand times, yet, in most of his observa- 
tions, powers magnifying only two or three hundred 
times were employed. The highest power of the Dor- 
pat telescope is only seven hundred, and yet the direc- 
tor of this instrument, Professor Struve, is of the opin- 
ion, that it is nearly or quite equal in quality, all things 
considered, to Herschel's forty-feet reflector. 

4 L. A. 


It is not generally understood in what way greatness 
of size in a telescope increases its powers ; and it con- 
veys but an imperfect idea of the excellence of a tele- 
scope, to tell how much it magnifies. In the same in- 
strument, an increase of magnifying power is always 
attended with a diminution of the light and of the field 
of view. Hence, the lower powers generally afford the 
most agreeable views, because they give the clearest 
light, and take in the largest space. The several cir- 
cumstances which influence the qualities of a telescope 
are, illuminating power, distinctness, field of view, and 
magnifying power. Large mirrors and large object- 
glasses are superior to smaller ones, because they collect 
a larger beam of light, and transmit it to the eye. Stars 
which are invisible to the naked eye are rendered visi- 
ble by the telescope, because this instrument collects 
and conveys to the eye a large beam of the few rays 
which emanate from the stars; whereas a beam of 
these rays of only the diameter of the pupil of the eye, 
would afford too little light for distinct vision. In this 
particular, large telescopes have great advantages over 
small ones. The great mirror of HerschePs forty-feet 
reflector collects and conveys to the eye a beam more 
than four feet in diameter. The Dorpat telescope also 
transmits to the eye a beam nine and one half inches 
in diameter. This seems small, in comparison with the 
reflector ; but much less of the light is lost on passing 
through the glass than is absorbed by the mirror, and 
the mirror is very liable to be clouded or tarnished ; 
so that there is not so great a difference in the two in- 
struments, in regard to illuminating power, as might be 
supposed from the difference of size. 

Distinctness of view is all-important to the perform- 
ance of an instrument. The object may be sufficiently 
bright, yet, if the image is distorted, or ill-defined, the 
illumination is of little consequence. This property 
depends mainly on the skill with which all the imper- 
fections of figure and color in the glass or mirror are 
corrected, and can exist in perfection only when the 


image is rendered completely achromatic, and when all 
the rays that proceed from each point in the object are 
collected into corresponding points of the image, un- 
accompanied by any other rays. Distinctness is very 
much affected by the steadiness of the instrument. 
Every one knows how indistinct a page becomes, when 
a book is passed rapidly backwards and forwards be- 
fore the eyes, and how difficult it is to read in a car- 
riage in rapid motion on a rough road. 

Field of view is another important consideration. 
The finest instruments exhibit the moon, for example, 
not only bright and distinct, in all its parts, but they 
take in the whole disk at once ; whereas, the inferior 
instruments, when the higher powers, especially, are ap- 
plied, permit us to see only a small part of the moon at 

I hope, my friend, that, when you have perused these 
Letters, or rather, while you are perusing them, you will 
have frequent opportunities of looking through a good 
telescope. I even anticipate that you will acquire such 
a taste for viewing the heavenly bodies with the aid of 
a good glass, that you will deem a telescope a most 
suitable appendage to your library, and as certainly not 
less an ornament to it than the more expensive statues 
with which some people of fortune adorn theirs. I 
will therefore, before concluding this letter, offer you 
a few directions for using the telescope. 

Some states of weather, even when the sky is clear, 
are far more favorable for astronomical observation than 
others. After sudden changes of temperature in the 
atmosphere, the medium is usually very unsteady. If 
the sun shines out warm after a cloudy season, the 
ground first becomes heated, and the air that is nearest 
to it is expanded, and rises, while the colder air de- 
scends, and thus ascending and descending currents of 
air, mingling together, create a confused and wavy me- 
dium. The same cause operates when a current of hot 
air rises from a chimney ; and hence the state of the 
atmosphere in cities and large towns is very unfavora- 


ble to the astronomer, on this account, as well as on 
account of the smoky condition in which it is usually 
found. After a long season of dry weather, also, the 
air becomes smoky, and unfit for observation. Indeed, 
foggy, misty, or smoky, air is so prevalent in some 
countries, that only a very few times in the whole year 
can be found, which are entirely suited to observation, 
especially with the higher powers ; for we must recol- 
lect, that these inequalities and imperfections are mag- 
nified by telescopes, as well as the objects themselves. 
Thus, as I have already mentioned, not more than one 
hundred good hours in a year could be obtained for 
observation with Herschel's great telescope. By good 
hours. Herschel means that the sky must be very clear, 
the moon absent, no twilight, no haziness, no violent 
wind, and no sudden change of temperature. As a 
general fact, the warmer climates enjoy a much finer 
sky for the astronomer than the colder, having many 
more clear evenings, a short twilight, and less change 
of temperature. The watery vapor of the atmosphere, 
also, is more perfectly dissolved in hot than in cold air, 
and the more water air contains, provided it is in a 
state of perfect solution, the clearer it is. 

A certain preparation of the observer himself is also 
requisite for the nicest observations with the telescope. 
He must be free from all agitation, and the eye must 
not recently have been exposed to a strong light, which 
contracts the pupil of the eye. Indeed, for delicate 
observations, the observer should remain for some time 
beforehand in a dark room, to let the pupil of the eye 
dilate. By this means, it will be enabled to admit a 
larger number of the rays of light. In ascending the 
stairs of an observatory, visiters frequently get out of 
breath, and having perhaps recently emerged from a 
strongly-lighted apartment, the eye is not in a favor- 
able state for observation. Under these disadvantages, 
they take a hasty look into the telescope, and it is no 
wonder that disappointment usually follows. 

Want of steadiness is a great difficulty attending the 


use of the highest magnifiers ; for the motions of the 
instrument are magnified as well as the object. Hence, 
in the structure of observatories, the greatest pains is 
requisite, to avoid all tremor, and to give to the instru- 
ments all possible steadiness ; and the same care is to 
be exercised by observers. In the more refined obser- 
vations, only one or two persons ought to be near the 

In general, low powers afford better views of the 
heavenly bodies than very high magnifiers. It may be 
thought absurd, to recommend the use of low powers, 
in respect to large instruments especially, since it is 
commonly supposed that the advantage of large instru- 
ments is, that they will bear high magnifying powers. 
But this is not their only, nor even their principal, ad- 
vantage. A good light and large field are qualities, for 
most purposes, more important than great magnifying 
power ; and it must be borne in mind, that, as we in- 
crease the magnifying power in a given instrument, we 
diminish both the illumination and the field of view. 
Still, different objects require different magnifying pow- 
ers ; and a telescope is usually furnished with several 
varieties of powers, one of which is best fitted for view- 
ing the moon, another for Jupiter, and a still higher 
power for Saturn. Comets require only the lowest 
magnifiers ; for here, our object is to command as much 
light, and as large a field, as possible, while it avails 
little to increase the dimensions of the object. On the 
other hand, for certain double stars, (stars which ap- 
pear single to the naked eye, but double to the tele- 
scope,) we require very high magnifiers, in order to 
separate these minute objects so far from each other, 
that the interval can be distinctly seen. Whenever we 
exhibit celestial objects to inexperienced observers, it 
is useful to precede the view with good drawings of 
the objects, accompanied by an explanation of what 
each appearance, exhibited in the telescope, indicates. 
The novice is told, that mountains and valleys can be 
seen in the moon by the aid of the telescope ; but, on 


looking, he sees a -confused mass of light and shade, 
and nothing which looks to him like either mountains 
or valleys. Had his attention been previously directed 
to a plain drawing of the moon, and each particular 
appearance interpreted to him, he would then have 
looked through the telescope with intelligence and 



" We, though from heaven remote, to heaven will move, 
With strength of mind, and tread the abyss above ; 
And penetrate, with an interior light, 
Those upper depths which Nature hid from sight. 
Pleased we will be, to walk along the sphere 
Of shining stars, and travel with the year." Ovid . 

AN observatory is a structure fitted up expressly for 
astronomical observations, and furnished with suitable 
instruments for that purpose. 

The two most celebrated observatories, hitherto built, 
are that of Tycho Brahe, and that of Greenwich, near 
London. The observatory of Tycho Brahe, Fig. 5, 
was constructed at the expense of the King of Den- 
mark, in a style of royal magnificence, and cost no less 
than two hundred thousand crowns. It was situated 
on the island of Huenna, at the entrance of the Baltic, 
and was called Uraniburg, or the palace of the skies. 

Before I give you an account of Tycho's observatory, 
I will recite a few particulars respecting this great as- 
tronomer himself. 

Tycho Brahe was of Swedish descent, and of noble 
family ; but having received his education at the Uni- 
versity of Copenhagen, and spent a large part of his life 
in Denmark, he is usually considered as a Dane, and 
quoted as a Danish astronomer. He was born in the 
year 1546. When he was about fourteen years old, 
there happened a great eclipse of the sun, which awak- 
ened in him a high interest, especially when he saw how 



Fig. 5. 


accurately all the circumstances of it answered to the 
prediction with which he had been before made ac- 
quainted. He was immediately seized with an irresisti- 
ble passion to acquire a knowledge of the science which 
could so successfully lift the veil of futurity. His friends 
had destined him for the profession of law, and, from 
the superior talents of which he gave early promise, and 
with the advantage of powerful family connexions, they 
had marked out for him a distinguished career in pub- 
lic life. They therefore endeavored to discourage him 
from pursuing a path which they deemed so much less 
glorious than that, and vainly sought, by various means, 
to extinguish the zeal for astronomy which was kindled 
in his youthful bosom. Despising all the attractions 
of a court, he contracted an alliance with a peasant girl, 
and, in the peaceful retirement of domestic life, desired 
no happier lot than to peruse the grand volume which 
the nocturnal heavens displayed to his enthusiastic im- 
agination. He soon established his fame as one of the 
greatest astronomers of the age, and monarchs did hom- 
age to his genius. The King of Denmark became his 
munificent patron, and James the First, King of Eng- 
land, when he went to Denmark to complete his mar- 
riage with a Danish Princess, passed eight days with 
Tycho in his observatory, and, at his departure, ad- 
dressed to the astronomer a Latin ode, accompanied 
with a magnificent present. He gave him also his royal 
license to print his works in England, and added to it 
the following complimentary letter : " Nor am I ac- 
quainted with these things on the relation of others, or 
from a mere perusal of your works, but I have seen 
them with my own eyes, and heard them with my own 
ears, in your residence at Uraniburg, during the various 
learned and agreeable conversations which I there held 
with you, which even now affect my mind to such a 
degree, that it is difficult to decide, whether I recollect 
them with greater pleasure or admiration." Admiring 
disciples also crowded to this sanctuary of the sciences, 
to acquire a knowledge of the heavens. 


The observatory consisted of a main building, which 
was square, each side being sixty feet, and of large 
wings in the form of round towers. The whole was 
executed in a style of great magnificence, and Tycho, 
who was a nobleman by descent, gratified his taste for 
splendor and ornament, by giving to every part of the 
structure an air of the most finished elegance. Nor 
were the instruments with which it was furnished less 
magnificent than the buildings. They were vastly 
larger than had before been employed in the survey of 
the heavens, and many of them were adorned with 
costly ornaments. The cut on page 46, Fig. 6, repre- 
sents one of Tycho's large and splendid instruments, 
(an astronomical quadrant,) on one side of which was 
figured a representation of the astronomer and his as- 
sistants, in the midst of their instruments, and intently 
engaged in making and recording observations. It con- 
veys to us a striking idea of the magnificence of his ar- 
rangements, and of the extent of his operations. 

Here Tycho sat in state, clad in the robes of nobili- 
ty, and supported throughout his establishment the eti- 
quette due to his rank. His observations were more 
numerous than all that had ever been made before, and 
they were carried to a degree of accuracy that is aston- 
ishing, when we consider that they were made without 
the use of the telescope, which was not yet invented. 

Tycho carried on his observations at Uraniburg for 
about twenty years, during which time he accumulated 
an immense store of accurate and valuable facts, which 
afforded the groundwork of the discovery of the great 
laws of the solar system established by Kepler, of whom 
I shall tell you more hereafter. 

But the high marks of distinction which Tycho en- 
joyed, not only from his own Sovereign, but also from 
foreign potentates, provoked the envy of the courtiers 
of his royal patron. They did not indeed venture to 
make their attacks upon him while his generous patron 
was living ; but the King was no sooner dead, and suc- 
ceeded by a young monarch, who did not feel the same 



Pig. 6. 


interest in protecting and encouraging this great orna- 
ment of the kingdom, than his envious foes carried into 
execution their long-meditated plot for his ruin. They 
represented to the young King, that the treasury was 
exhausted, and that it was necessary to retrench a num- 
ber of pensions, which had been granted for useless 
purposes, and in particular that of Tycho, which, they 
maintained, ought to be conferred upon some person 
capable of rendering greater services to the state. By 
these means, they succeeded in depriving him of his 
support, and he was compelled to retreat under the 
hospitable mansion of a friend in Germany. Here he 
became known to the Emperor, who invited him to 
Prague, where, with an ample stipend, he resumed his 
labors. But, though surrounded with affectionate friends 
and admiring disciples, he was still an exile in a foreign 
land. Although his country had been base in its in- 
gratitude, it was yet the land which he loved ; the 
scene of his earliest affection ; the theatre of his scien- 
tific glory. These feelings continually preyed upon his 
mind, and his unsettled spirit was ever hovering among 
his native mountains. In this condition he was at- 
tacked by a disease of the most painful kind, and, 
though its agonizing paroxysms had lengthened inter- 
missions, yet he saw that death was approaching. He 
implored his pupils to persevere in their scientific la- 
bors ; he conversed with Kepler on some of the pro- 
foundest points of astronomy ; and with these secular 
occupations he mingled frequent acts of piety and de- 
votion. In this happy condition he expired, without 
pain, at the age of fifty-five.* 

The observatory at Greenwich was not built until a 
hundred years after that of Tycho Brahe, namely, in 
1676. The great interests of the British nation, which 
are involved in navigation, constituted the ruling motive 
with the government to lend their aid in erecting and 
maintaining this observatory. 

* Brewster's Life of Newton. 


The site of the observatory at Greenwich is on a 
commanding eminence facing the River Thames, five 
miles east of the central parts of London. Being part 
of a royal park, the neighboring grounds are in no dan- 
ger of being occupied by buildings, so as to obstruct the 
view. It is also in full view of the shipping on the 
Thames ; and, according to a standing regulation of the 
observatory, at the instant of one o'clock, every day, a 
huge ball is dropped from over the house, as a signal 
to the commanders of vessels for regulating their chro- 

The buildings comprise a series of rooms, of sufficient 
number and extent to accommodate the different instru- 
ments, the inmates of the establishment, and the libra- 
ry ; and on the top is a celebrated camera obscura, ex- 
hibiting a most distinct and perfect picture of the grand 
and unrivalled scenery which this eminence commands. 

This establishment, by the accuracy and extent of 
its observations, has contributed more than all other in- 
stitutions to perfect the science of astronomy. 

To preside over and direct this great institution, a 
man of the highest eminence in the science is appoint- 
ed by the government, with the title of Astronomer 
Royal. He is paid an ample salary, with the under- 
standing that he is to devote himself exclusively to the 
business of the observatory. The astronomers royal of 
the Greenwich observatory, from the time of its first 
establishment, in 1676, to the present time, have con- 
stituted a series of the proudest names of which Brit- 
ish science can boast. A more detailed sketch of their 
interesting history will be given towards the close of 
these Letters. 

Six assistants, besides inferior laborers, are constant- 
ly in attendance ; and the business of making and re- 
cording observations is conducted with the utmost sys- 
tem and order. 

The great objects to be attained in the construction 
of an observatory are, a commanding and unobstructed 
view of the heavens ; freedom from causes that affect 


the transparency and uniform state of the atmosphere, 
such as fires, smoke, or marshy grounds ; mechanical 
facilities for the management of instruments, and, es- 
pecially, every precaution that is necessary to secure 
perfect steadiness. This last consideration is one of the 
greatest importance, particularly in the use of very large 
magnifiers ; for we must recollect, that any motion in 
the instrument is magnified by the full power of the 
glass, and gives a proportional unsteadiness to the ob- 
ject. A situation is therefore selected as remote as pos- 
sible from public roads, (for even the passing of carriages 
would give a tremulous motion to the ground, which 
would be sensible in large instruments,) and structures 
of solid masonry are commenced deep enough in the 
ground to be unaffected by frost, and built up to the 
height required, without any connexion with the other 
parts of the building. Many observatories are furnish- 
ed with a movable dome for a roof, capable of revolving 
on rollers, so that instruments penetrating through the 
roof may be easily brought to bear upon any point at 
or near the zenith. 

You will not perhaps desire me to go into a minute 
description of all the various instruments that are used 
in a well-constructed observatory. Nor is this neces- 
sary, since a very large proportion of all astronomical 
observations are taken on the meridian, by means of the 
transit instrument and clock. When a body, in its di- 
urnal revolution, comes to the meridian, it is at its high- 
est point above the horizon, and is then least affected 
by refraction and parallax. This, then, is the most fa- 
vorable position for taking observations upon it. More- 
over, it is peculiarly easy to take observations on a body 
when in this situation. Hence the transit instrument 
and clock are the most important members of an astro- 
nomical observatory. You will, therefore, expect me 
to give you some account of these instruments. 

The transit instrument is a telescope which is fixed 
permanently in the meridian, and moves only in that 
plane. The accompanying diagram, Fig. 7, represents 

5 L. A. 


a side view of a portable transit instrument, exhibiting 
the telescope supported on a firm horizontal axis, on 
which it turns in the plane of the meridian, from the 
south point of the horizon through the zenith to the 
north point. It can therefore be so directed as to ob- 
serve the passage of a star across the meridian at any 
altitude. The accompanying graduated circle enables 

Fig. 7. 

the observer to set the instrument at any required alti- 
tude, corresponding to the known altitude at which the 
body to be observed crosses the meridian. Or it may 
be used to measure the altitude of a body, or its zenith 
distance, at the time of its meridian passage. Near the 
circle may be seen a spirit-level, which serves to show 
when the axis is exactly on a level with the horizon. 
The framework is made of solid metal, (usually brass,) 
every thing being arranged with reference to keeping 
the instrument perfectly steady. It stands on screws, 
which not only afford a steady support, but are useful 


for adjusting the instrument to a perfect level. The 
transit instrument is sometimes fixed immovably to a 
solid foundation, as a pillar of stone, which is built up 
from a depth in the ground below the reach of frost. 
When enclosed in a building, as in an observatory, the 
stone pillar is carried up separate from the walls and 
floors of the building, so as to be entirely free from 
the agitations to which they are liable. 

The use of the transit instrument is to show the 
precise instant when a heavenly body is on the me- 
ridian, or to measure the time it occupies in crossing 
the meridian. The astronomical clock is the constant 
companion of the transit instrument. This clock is so 
regulated as to keep exact pace with the stars, and of 
course with the revolution of the earth on its axis ; that 
is, i^ is regulated to sidereal time. It measures the 
progress of a star, indicating an hour for every fifteen 
degrees, and twenty-four hours for the whole period of 
the revolution of the star. Sidereal time commences 
when the vernal equinox is on the meridian, just as 
solar time commences when the sun is on the meridian. 
Hence the hour by the sidereal clock has no correspon- 
dence with the hour of the day, but simply indicates how 
long it is since the equinoctial point crossed the merid- 
ian. For example, the clock of an observatory points 
to three hours and twenty minutes ; this may be in the 
morning, at noon, or any other time of the day, for it 
merely shows that it is three hours and twenty minutes 
since the equinox was on the meridian. Hence, when a 
star is on the meridian, the clock itself shows its right 
ascension, which you will recollect is the angular dis- 
tance measured on the equinoctial, from the point of 
intersection of the ecliptic and equinoctial, called the 
vernal equinox, reckoning fifteen degrees for every hour, 
and a proportional number of degrees and minutes for a 
less period. I have before remarked, that a very large 
portion of all astronomical observations are taken when 
the bodies are on the meridian, by means of the transit 
instrument and clock. 


Having now described these instruments, I will next 
explain the manner of using them for different obser- 
vations. Any thing becomes a measure of time, which 
divides duration equally. The equinoctial, therefore, is 
peculiarly adapted to this purpose, since, in the daily 
revolution of the heavens, equal portions of the equi- 
noctial pass under the meridian in equal times. The 
only difficulty is, to ascertain the amount of these por- 
tions for given intervals. Now, the clock shows us 
exactly this amount; for, when regulated to sidereal 
time, (as it easily may be,) the hour-hand keeps ex- 
act pace with the equator, revolving once on the dial- 
plate of the clock while the equator turns once by the 
revolution of the earth. The same is true, also, of all 
the small circles of diurnal revolution ; they all turn 
exactly at the same rate as the equinoctial, and a star 
situated any where between the equator and the pole 
will move in its diurnal circle along with the clock, in 
the same manner as though it were in the equinoctial. 
Hence, if we note the interval of time between the pas- 
sage of any two stars, as shown by the clock, we have 
a measure of the number of degrees by which they are 
distant from each other in right ascension. Hence we 
see how easy it is to take arcs of right ascension : the 
transit instrument shows us when a body is on the me- 
ridian ; the clock indicates how long it is since the 
vernal equinox passed it, which is the right ascension 
itself; or it tells us the difference of right ascension 
between any two bodies, simply by indicating the differ- 
ence in time between their periods of passing the merid- 
ian. Again, it is easy to take the declination of a body 
when on the meridian. By declination, you will recol- 
lect, is meant the distance of a heavenly body from the 
equinoctial ; the same, indeed, as latitude on the earth. 
When a star is passing the meridian, if, on the instant 
of crossing the meridian wire of the telescope, we take 
its distance from the north pole, (which may readily be 
done, because the position of the pole is always known, 
being equal to the latitude of the place,) and subtract 


this distance from ninety degrees, the remainder will be 
the distance from the equator, which is the declination. 
You will ask, why we take this indirect method of find- 
ing the declination ? Why we do not rather take the 
distance of the star from the equinoctial, at once ? I 
answer, that it is easy to point an instrument to the 
north pole, and to ascertain its exact position, and of 
course to measure any distance from it on the meridian, 
while, as there is nothing to mark the exact situation 
of the equinoctial, it is not so easy to take direct meas- 
urements from it. When we have thus determined 
the situation of a heavenly body, with respect to two 
great circles at right angles with each other, as in the 
present case, the distance of a body from the equator 
and from the equinoctial colure, or that meridian which 
passes though the vernal equinox, we know its relative 
position in the heavens ; and when we have thus de- 
termined the relative positions of all the stars, we may 
lay them down on a map or a globe, exactly as we do 
places on the earth, by means of their latitude and lon- 

The foregoing is only a specimen of the various uses 
of the transit instrument, in finding the relative places 
of the heavenly bodies. Another use of this excellent 
instrument is, to regulate our clocks and watches. By 
an observation with the transit instrument, we find 
when the sun's centre is on the meridian. This is the 
exact time of apparent noon. But watches and clocks 
usually keep mean time, and therefore, in order to set 
our timepiece by the transit instrument, we must apply 
to the apparent time of noon the equation of time, as 
will be explained in my next Letter. 

A noon-mark may easily be made by the aid of the 
transit instrument. A window sill is frequently selected 
as a suitable place for the mark, advantage being taken 
of the shadow projected upon it by the perpendicular 
casing of the window. Let an assistant stand, with a 
rule laid on the line of shadow, and with a knife ready 
to make the mark, the instant when the observer at the 


transit instrument announces that the centre of the sun 
is on the meridian. By a concerted signal, as the 
stroke of a bell, the inhabitants of a town may all fix 
a noon-mark from the same observation. If the signal 
be given on one of the days when apparent time and 
mean time become equal to each other, as on the twen- 
ty-fourth of December, no equation of time is required. 

As a noon-mark is convenient for regulating time- 
pieces, I will point out a method of making one, which 
may be practised without the aid of the telescope. 
Upon a smooth, level plane, freely exposed to the sun, 
with a pair of compasses describe a circle. In the cen- 
tre, where the leg of the compasses stood, erect a per- 
pendicular wire of such a length, that the termination 
of its shadow shall fall upon the circumference of the 
circle at some hour before noon, as about ten o'clock. 
Make a small dot at the point where the end of the 
shadow falls upon the circle, and do the same where it 
falls upon it again in the afternoon. Take a point half- 
way between these two points, and from it draw a line 
to the centre, and it will be a true meridian line. The 
direction of this line would be the same, whether it 
were made in the Summer or in the Winter ; but it is 
expedient to draw it about the fifteenth of June, for then 
the shadow alters its length most rapidly, and the mo- 
ment of its crossing the wire will be more definite, 
than in the Winter. At this time of year, also, the sun 
and clock agree, or are together, as will be more fully ex- 
plained in my next Letter ; whereas, at other times of 
the year, the time of noon, as indicated by a common 
clock, would not agree with that indicated by the sun. 
If the upper end of the wire is flattened, and a small 
hole is made in it, through which the sun may shine, 
the instant when this bright spot falls upon the circle 
will be better defined than the termination of the shadow. 

Another important instrument of the observatory is 
the mural circle. It is a graduated circle, usually of 
very large size, fixed permanently in the plane of the 
meridian, and attached firmly to a perpendicular wall ; 


and on its centre is a telescope, which revolves along 
with it, and is easily brought to bear on any object in 
any point in the meridian. It is made of large size, 
sometimes twenty feet in diameter, in order that very 
small angles may be measured on its limb ; for it is ob- 
vious that a small angle, as one second, will be a larger 
space on the limb of an instrument, in proportion as 
the instrument itself is larger. The vertical circle usu- 
ally connected with the transit instrument, as in Fig. 7, 
may indeed be employed for the same purposes as the 
mural circle, namely, to measure arcs of the meridian, 
as meridian altitudes, zenith distances, north polar dis- 
tances, and declinations ; but as that circle must nec- 
essarily be small, and therefore incapable of measuring 
very minute angles, the mural circle is particularly use- 
ful in measuring these important arcs. It is very diffi- 
cult to keep so large an instrument perfectly steady ; 
and therefore it is attached to a massive wall of solid 
masonry, and is hence called a mural circle, from a 
Latin word, (murus,) which signifies a wall. 

The diagram, Fig. 8, page 56, represents a mural 
circle fixed to its wall, and ready for observations. It 
will be seen, that every expedient is employed to give 
the instrument firmness of parts and steadiness of posi- 
tion. The circle is of solid metal, usually of brass, and 
it is strengthened by numerous radii, which keep it from 
warping or bending ; and these are made in the form 
of hollow cones, because that is the figure which unites 
in the highest degree lightness and strength. On the 
rim of the instrument, at A, you may observe a micro- 
scope. This is attached to a micrometer, a delicate 
piece of apparatus, used for reading the minute subdi- 
visions of angles ; for, after dividing the limb of the 
instrument as minutely as possible, it will then be nec- 
essary to magnify those divisions with the microscope, 
and subdivide each of these parts with the micrometer. 
Thus, if we have a mural circle twenty feet in diame- 
ter, and of course nearly sixty-three feet in circumfer- 
ence, since there are twenty-one thousand and six hun- 


dred minutes in the whole circle, we shall find, by cal- 
culation, that one minute would occupy, on the limb of 
such an instrument, only about one thirtieth of an inch, 
and a second, only one eighteen hundredth of an inch. 
We could not, therefore, hope to carry the actual di- 
visions to a greater degree of minuteness than minutes ; 
but each of these spaces may again be subdivided into 
seconds by the micrometer. 

Fig. 8. 

From these statements, you will acquire some faint 
idea of the extreme difficulty of making perfect astro- 
nomical instruments, especially where they are intended 
to measure such minute angles as one second. Indeed, 
the art of constructing astronomical instruments is one 
which requires such refined mechanical genius, so su- 


perior a mind to devise, and so delicate a hand to ex- 
ecute, that the most celebrated instrument-makers 
take rank with the most distinguished astronomers ; 
supplying, as they do, the means by which only the 
latter are enabled to make these great discoveries. As- 
tronomers have sometimes made their own telescopes ; 
but they have seldom, if ever, possessed the refined 
manual skill which is requisite for graduating delicate 

The sextant is also one of the most valuable instru- 
ments for taking celestial arcs, or the distance between 
any two points on the celestial sphere, being applicable 
to a much greater number of purposes than the instru- 
ments already described. It is particularly valuable for 
measuring celestial arcs at sea, because it is not, like 
most astronomical instruments, affected by the motion 
of the ship. The principle of the sextant may be briefly 
described, as follows : it gives the angular distance be- 
tween any two bodies on the celestial sphere, by reflect- 
ing the image of one of the bodies so as to coincide 
with the other body, as seen directly. The arc through 
which the reflector is turned, to bring the reflected body 
to coincide with the other body, becomes a measure of 
the angular distance between them. By keeping this 
principle in view, you will be able to understand the 
use of the several parts of the instrument, as they are 
exhibited in the diagram, Fig. 9, page 58. 

It is, you observe, of a triangular shape, and it is 
made strong and firm by metallic cross-bars. It has two 
reflectors, I and H, called, respectively, the index glass 
and the horizon glass, both of which are firmly fixed 
perpendicular to the plane of the instrument. The 
index glass is attached to the movable arm, I D, and 
turns as this is moved along the graduated limb, E F. 
This arm also carries a vernier, at D, a contrivance 
which, like the micrometer, enables us to take off mi- 
nute parts of the spaces into which the limb is divided. 
The horizon glass, H, consists of two parts ; the upper 
part being transparent or open, so that the eye, looking 



Fig. 9. 

through the telescope, T, can see through it a distant 
body, as a star at S, while the lower part is a reflector. 
Suppose it were required to measure the angular dis- 
tance between the moon and a certain star, the rnoon 
being at M, and the star at S. The instrument is held 
firmly in the hand, so that the eye, looking through the 
telescope, sees the star, S, through the transparent part 
of the horizon glass. Then the movable arm, I D, is 
moved from F towards E, until the image of M is re- 
flected down to S, when the number of degrees and 
parts of a degree reckoned on the limb, from F to the 
index at D, will show the angular distance between the 
two bodies. 




" From old Eternity's mysterious orb 
Was Time cut off, and cast beneath the skies." Young. 

HAVING hitherto been conversant only with the many 
fine and sentimental things which the poets have sung 
respecting Old Time, perhaps you will find some diffi- 
culty in bringing down your mind to the calmer con- 
sideration of what time really is, and according to what 
different standards it is measured for different purposes. 
You will not, however, I think, find the subject even 
in our matter-of-fact and unpoetical way of treating it, 
altogether uninteresting. What, then, is time? Time 
is a measured portion of indefinite duration. It con- 
sists of equal portions cut off from eternity, as a line on 
the surface of the earth is separated from its contiguous 
portions that constitute a great circle of the sphere, by 
applying to it a two-foot scale ; or as a few yards of 
cloth are measured off from a piece of unknown or in- 
definite extent. 

Any thing, or any event which takes place at equal 
intervals, may become a measure of time. Thus, the 
pulsations of the wrist, the flowing of a given quantity 
of sand from one vessel to another, as in the hourglass, 
the beating of a pendulum, and the revolution of a star, 
have been severally employed as measures of time. But 
the great standard of time is the period of the revolu- 
tion of the earth on its axis, which, by the most exact 
observations, is found to be always the same. I have 
anticipated a little of this subject, in giving an account 
of the transit instrument and clock, but I propose, in 
this letter, to enter into it more at large. 

The time of the earth's revolution on its axis, as al- 
ready explained, is called a sidereal day, and is deter- 
mined by the revolution of a star in the heavens. This 


interval is divided into twenty-four sidereal hours. Ob- 
servations taken on numerous stars, in different ages 
of the world, show that they all perform their diurnal 
revolution in the same time, and that their motion, dur- 
ing any part of the revolution, is always uniform. Here, 
then, we have an exact measure of time, probably more 
exact than any thing which can be devised by art. 
Solar time is reckoned by the apparent revolution of 
the sun from the meridian round to the meridian again. 
Were the sun stationary in the heavens, like a fixed 
star, the time of its apparent revolution would be equal 
to the revolution of the earth on its axis, and the solar 
and the sidereal days would be equal. But, since the 
sun passes from west to east, through three hundred and 
sixty degrees, in three hundred and sixty-five and one 
fourth days, it moves eastward nearly one degree a day. 
While, therefore, the earth is turning round on its axis, 
the sun is moving in the same direction, so that, when 
we have come round under the same celestial meridian 
from which we started, we do not find the sun there, 
but he has moved eastward nearly a degree, and the 
earth must perform so much more than one complete 
revolution, before we come under the sun again. Now, 
since we move, in the diurnal revolution, fifteen de- 
grees in sixty minutes, we must pass over one degree 
in four minutes. It takes, therefore, four minutes for 
us to catch up with the sun, after we have made one 
complete revolution. Hence the solar day is about four 
minutes longer than the sidereal ; and if we were to reck- 
on the sidereal day twenty-four hours, we should reckon 
the solar day twenty-four hours four minutes. To suit 
the purposes of society at large, however, it is found more 
convenient to reckon the solar days twenty-four hours, 
and throw the fraction into the sidereal day. Then, 

24h. 4m. : 24h. : : 24h. : 23h. 56m. 4s. 
That is, when we reduce twenty-four hours and four 
minutes to twenty-four hours, the same proportion will 
require that we reduce the sidereal day from twenty-four 
hours to twenty-three hours fifty-six minutes four sec- 


onds ; or, in other words, a sidereal day is such a part 
of a solar day. The solar days, however, do not always 
differ from the sidereal by precisely the same fraction, 
since they are not constantly of the same length. Time, 
as measured by the sun, is called apparent time, and 
a clock so regulated as always to keep exactly with the 
sun, is said to keep apparent time. Mean time is time 
reckoned by the average length of all the solar days 
throughout the year. This is the period which consti- 
tutes the civil day of twenty-four hours, beginning when 
the sun is on the lower meridian, namely, at twelve 
o'clock at night, and counted by twelve hours from the 
lower to the upper meridian, and from the upper to the 
lower. The astronomical day is the apparent solar 
day counted through the whole twenty-four hours, (in- 
stead of by periods of twelve hours each, as in the civil 
day,) and begins at noon. Thus it is now the tenth 
of June, at nine o'clock, A. M., according to civil time ; 
but we have not yet reached the tenth of June by as- 
tronomical time, nor shall we, until noon to-day ; con- 
sequently, it is now June ninth, twenty-first hour of 
astronomical time. Astronomers, since so many of their 
observations are taken on the meridian, are always sup- 
posed to look towards the south. Geographers, having 
formerly been conversant only with the northern hem- 
isphere, are always understood to be looking towards 
the north. Hence, left and right, when applied to the 
astronomer, mean east and west, respectively ; but to 
the geographer the right is east, and the left, west. 

Clocks are usually regulated so as to indicate mean 
solar time ; yet, as this is an artificial period not marked 
off, like the sidereal day, by any natural event, it is 
necessary to know how much is to be added to, or sub- 
tracted from, the apparent solar time, in order to give 
the corresponding mean time. The interval, by which 
apparent time differs from mean time, is called the equa- 
tion of time. If one clock is so constructed as to keep 
exactly with the sun, going faster or slower, according 
as the lengths of the solar days vary, and another clock 

6 L. A. 


is regulated to mean time, then the difference of the 
two clocks, at any period, would be the equation of time 
for that moment. If the apparent clock were faster 
than the mean, then the equation of time must be sub- 
tracted ; but if the apparent clock were slower than the 
mean, then the equation of time must be added, to give 
the mean time. The two clocks would differ most about 
the third of November, when the apparent tirade is six- 
teen and one fourth minutes greater than the mean. 
But since apparent time is sometimes greater and some- 
times less than mean time, the two must obviously be 
sometimes equal to each other. This is, in fact, the 
case four times a year, namely, April fifteenth, June 
fifteenth, September first, and December twenty-fourth. 

Astronomical clocks are made of the best workman- 
ship, with every advantage that can promote their reg- 
ularity. Although they are brought to an astonishing 
degree of accuracy, yet they are not as regular in their 
movements as the stars are, and their accuracy requires 
to be frequently tested. The transit instrument itself, 
when once accurately placed in the meridian, affords 
the means of testing the correctness of the clock, since 
one revolution of a star, from the meridian to the me- 
ridian again, ought to correspond exactly to twenty-four 
hours by the clock, and to continue the same, from day 
to day ; and the right ascensions of various stars, as they 
cross the meridian, ought to be such by the clock, as 
they are given in the tables, where they are stated ac- 
cording to the accurate determinations of astronomers. 
Or, by taking the difference of any two stars, on suc- 
cessive days, it will be seen whether the going of the 
clock is uniform for that part of the day ; and by taking 
the right ascensions of different pairs of stars, we may 
learn the rate of the clock at various parts of the day. 
We thus learn, not only whether the clock accurately 
measures the length of the sidereal day, but also whether 
it goes uniformly from hour to hour. 

Although astronomical clocks have been brought to 
a great degree of perfection, so as hardly to vary a sec- 


ond for many months, yet none are absolutely perfect, 
and most are so far from it, as to require to be corrected 
by means of the transit instrument, every few days. 
Indeed, for the nicest observations, it is usual not to 
attempt to bring the clock to a state of absolute correct- 
ness, but, after bringing it as near to such a state as can 
conveniently be done, to ascertain how much it gains 
or loses in a day ; that is, to ascertain the rate of its 
going, and to make allowance accordingly. 

Having considered the manner in which the smaller 
divisions of time are measured, let us now take a hasty 
glance at the larger periods which compose the calen- 

As a day is the period of the revolution of the earth 
on its axis, so a year is the period of the revolution of 
the earth around the sun. This time, which constitutes 
the astronomical year, has been ascertained with great 
exactness, and found to be three hundred and sixty-five 
days five hours forty-eight minutes and fifty-one sec- 
onds. The most ancient nations determined the num- 
ber of days in the year by means of the stylus, a per- 
pendicular rod which casts its shadow on a smooth 
plane bearing a meridian line. The time when the 
shadow was shortest, would indicate the day of the 
Summer solstice ; and the number of days which elaps- 
ed, until the shadow returned to the same length again, 
would show the number of days in the year. This was 
found to be three hundred and sixty-five whole days, 
and accordingly, this period was adopted for the civil 
year. Such a difference, however, between the civil 
and astronomical years, at length threw all dates into 
confusion. For if, at first, the Summer solstice hap- 
pened on the twenty-first of June, at the end of four 
years, the sun would not have reached the solstice until 
the twenty-second of June ; that is, it would have been 
behind its time. At the end of the next four years, the 
solstice would fall on the twenty-third ; and in process 
of time, it would fall successively on every day of the 
year. The same would be true of any other fixed date. 


Julius Caesar, who was distinguished alike for the 
variety and extent of his knowledge, and his skill in 
arms, first attempted to make the calendar conform to 
the motions of the sun. 

" Amidst the hurry of tumultuous war, 

The stars, the gods, the heavens, were still his care." 

Aided by Sosigenes, an Egyptian astronomer, he 
made the first correction of the calendar, by introducing 
an additional day every fourth year, making February 
to consist of twenty-nine instead of twenty-eight days, 
and of course the whole year to consist of three hundred 
and sixty-six days. This fourth year was denominated 
Bissextile, because the sixth day before the Kalends of 
March was reckoned twice. It is also called Leap Year. 

The Julian year was introduced into all the civilized 
nations that submitted to the Roman power, and con- 
tinued in general use until the year 1582. But the 
true correction was not six hours, but five hours forty- 
nine minutes ; hence the addition was too great by 
eleven minutes. This small fraction would amount in 
one hundred years to three fourths of a day, and in 
one thousand years to more than seven days. From 
the year 325 to the year 1582, it had, in fact, amount- 
ed to more than ten days ; for it was known that, in 
325, the vernal equinox fell on the twenty-first of 
March, whereas, in 1582, it fell on the eleventh. It 
was ordered by the Council of Nice, a celebrated eccle- 
siastical council, held in the year 325, that Easter should 
be celebrated upon the first Sunday after the first full 
moon, next following the vernal equinox ; and as cer- 
tain other festivals of the Romish Church were appointed 
at particular seasons of the year, confusion would result 
from such a want of constancy between any fixed date 
and a particular season of the year. Suppose, for ex- 
ample, a festival accompanied by numerous religious 
ceremonies, was decreed by the Church to be held at 
the time when the sun crossed the equator in the Spring, 
(an event hailed with great joy, as the harbinger of the 
return of Summer,) and that, in the year 325, March 


twenty-first was designated as the time for holding the 
festival, since, at that period, it was on the twenty-first 
of March when the sun reached the equinox ; the next 
year, the sun would reach the equinox a little sooner 
than the twenty-first of March, only eleven minutes, in- 
deed, but still amounting in twelve hundred years to 
ten days ; that is, in 1582, the sun reached the equinox 
on the eleventh of March. If, therefore, they should 
continue to observe the twenty-first as a religious festival 
in honor of this event, they would commit the absurdity 
of celebrating it ten days after it had passed by. Pope 
Gregory the Thirteenth, who was then at the head of the 
Roman See, was a man of science, and undertook to 
reform the calendar, so that fixed dates would always 
correspond to the same seasons of the year. He first 
decreed, that the year should be brought forward ten 
days, by reckoning the fifth of October the fifteenth ; 
and, in order to prevent the calendar from falling into 
confusion afterwards, he prescribed the following rule : 
Every year whose number is not divisible by four, 
without a remainder, consists of three hundred and 
sixty-five days ; every year which is so divisible, but 
is not divisible by one hundred, of three hundred and 
sixty-six; every year divisible by one hundred, but 
not by four hundred, again, of three hundred and six- 
ty-five ; and every year divisible by four hundred, of 
three hundred and sixty-six. 

Thus the year 1838, not being divisible by four, con- 
tains three hundred and sixty-five days, while 1836 and 
1840 are leap years. Yet, to make every fourth year 
consist of three hundred and sixty-six days would in- 
crease it too much, by about three fourths of a day in 
a century ; therefore every hundredth year has only 
three hundred and sixty-five days. Thus 1800, although 
divisible by four, was not a leap year, but a common 
year. But we have allowed a whole day in a hundred 
years, whereas we ought to have allowed only three 
fourths of a day. Hence, in four hundred years, we 
should allow a day too much, and therefore, we let the 


four hundredth remain a leap year. This rule involves 
an error of less than a day in four thousand two hun- 
dred and thirty-seven years. 

The Pope, who, you will recollect, at that age as- 
sumed authority over all secular princes, issued his de- 
cree to the reigning sovereigns of Christendom, com- 
manding the observance of the calendar as reformed by 
him. The decree met with great opposition among the 
Protestant States, as they recognised in it a new exer- 
cise of ecclesiastical tyranny ; and some of them, when 
they received it, made it expressly understood, that their 
acquiescence should not be construed as a submission 
to the Papal authority. 

In 1752, the Gregorian year, or New Style, was es- 
tablished in Great Britain by act of Parliament ; and the 
dates of all deeds, and other legal papers, were to be 
made according to it. As above a century had then 
passed since the first introduction of the new style, elev- 
en days were suppressed, the third of September being 
called the fourteenth. By the same act, the begin- 
ning of the year was changed from March twenty-fifth 
to January first. A few persons born previously to 
1752 have come down to our day, and we frequently 
see inscriptions on tombstones of those whose time of 
birth is recorded in old style. In order to make this 
correspond to our present mode of reckoning, we must 
add eleven days to the date. Thus the same event 
would be June twelfth of old style, or June twenty-third 
of new style ; and if an event occurred between January 
first and March twenty-fifth, the date of the year would 
be advanced one, since February 1st, 1740, O. S. would 
be February 1st, 1741, N. S. Thus, General Wash- 
ington was born February 1 1th, 1731, O. S., or February 
22d, 1732, N. S. If we inquire how any present event 
may be made to correspond in date to the old style, 
we must subtract twelve days, and put the year back 
one, if the event lies between January first and March 
twenty-fifth. Thus, June tenth, N. S. corresponds to 
May twenty-ninth, O. S. ; and March 20th, 1840, to 


March 8th, 1839. France, being a Roman Catholic 
country, adopted the new style soon after it was decreed 
by the Pope ; but Protestant countries, as we have seen, 
were much slower in adopting it ; and Russia, and the 
Greek Church generally, still adhere to the old style. 
In order, therefore, to make the Russian dates corres- 
pond to ours, we must add to them twelve days. 

It may seem to you very remarkable, that so much 
pains should have been bestowed upon this subject ; but 
without a correct and uniform standard of time, the 
dates of deeds, commissions, and all legal papers ; of 
fasts and festivals, appointed by ecclesiastical authority ; 
the returns of seasons, and the records of history, must 
all fall into inextricable confusion. To change the ob- 
servance of certain religious feasts, which have been 
long fixed to particular days, is looked upon as an im- 
pious innovation ; and though the times of the events, 
upon which these ceremonies depend, are utterly un- 
known, it is still insisted upon by certain classes in 
England, that the Glastenbury thorn blooms on Christ- 
mas day. 

Although the ancient Grecian calendar was extremely 
defective, yet the common people were entirely averse 
to its reformation. Their superstitious adherence to 
these errors was satirized by Aristophanes, in his com- 
edy of the Clouds. An actor, who had just come from 
Athens, recounts that he met with Diana, or the moon, 
and found her extremely incensed, that they did not 
regulate her course better. She complained, that the 
order of Nature was changed, and every thing turned 
topsyturvy. The gods no longer knew what belonged 
to them ; but, after paying their visits on certain feast- 
days, and expecting to meet with good cheer, as usual, 
they were under the disagreeable necessity of returning 
back to heaven without their suppers. 

Among the Greeks, and other ancient nations, the 
length of the year was generally regulated by the course 
of the moon. This planet, on account of the different 
appearances which she exhibits at her full, change, and 


quarters, was considered by them as best adapted of 
any of the celestial bodies for this purpose. As one 
lunation, or revolution of the moon around the earth, 
was found to be completed in about twenty-nine and 
one half days, and twelve of these periods being sup- 
posed equal to one revolution of the sun, their months 
were made to consist of twenty-nine and thirty days al- 
ternately, and their year of three hundred and fifty-four 
days. But this disagreed with the annual revolution 
of the sun, which must evidently govern the seasons of 
the year, more than eleven days. The irregularities, 
which such a mode of reckoning would occasion, must 
have been too obvious not to have been observed. For, 
supposing it to have been settled, at any particular time, 
that the beginning of the year should be in the Spring ; 
in about sixteen years afterwards, the beginning would 
have been in Autumn ; and in thirty-three or thirty-four 
years, it would have gone backwards through all the 
seasons, to Spring again. This defect they attempted 
to rectify, by introducing a number of days, at certain 
times, into the calendar, as occasion required, and put- 
ting the beginning of the year forwards, in order to make 
it agree with the course of the sun. But as these ad- 
ditions, or intercalations, as they were called, were 
generally consigned to the care of the priests, who, from 
motives of interest or superstition, frequently omitted 
them, the year was made long or short at pleasure. 

The week is another division of time, of the highest 
antiquity, which, in almost all countries, has been made 
to consist of seven days ; a period supposed by some 
to have been traditionally derived from the creation of 
the world ; while others imagine it to have been regu- 
lated by the phases of the moon. The names, Satur- 
day, Sunday, and Monday, are obviously derived from 
Saturn, the Sun, and the Moon ; while Tuesday, 
Wednesday, Thursday, and Friday, are the days of 
Tuisco, Woden, Thor, and Friga, which are Saxon 
names for Mars, Mercury, Jupiter, and Venus.* 

* Bonnycastle's Astronomy. 


The common year begins and ends on the same day 
of the week ; but leap year ends one day later than it 
began. Fifty- two weeks contain three hundred and 
sixty-four days ; if, therefore, the year begins on Tues- 
day, for example, we should complete fifty-two weeks on 
Monday, leaving one day, (Tuesday,) to complete the 
year, and the following year would begin on Wednes- 
day. Hence, any day of the month is one day later in 
the week, than the corresponding day of the preceding 
year. Thus, if the sixteenth of November, 1838, falls 
on Friday, the sixteenth of November, 1837, fell on 
Thursday, and will fall, in 1839, on Saturday. But if 
leap year begins on Sunday, it ends on Monday, and 
the following year begins on Tuesday ; while any given 
day of the month is two days later in the week than the 
corresponding date of the preceding year. 



" He took the golden compasses, prepared 
In God's eternal store, to circumscribe 
This universe, and all created things ; 
One foot he centred, and the other turned 
Round through the vast profundity obscure, 
And said, ' Thus far extend, thus far thy bounds, 
This be thy just circumference, O World !' "Milton. 

IN the earliest ages, the earth was regarded as one 
continued plane ; but, at a comparatively remote period, 
as five hundred years before the Christian era, astrono- 
mers began to entertain the opinion that the earth is 
round. We are able now to adduce various arguments 
which severally prove this truth. First, when a ship is 
coming in from sea, we first observe only the very high- 
est parts of the ship, while the lower portions come suc- 
cessively into view. Were the earth a continued plane, 
the lower parts of the ship would be visible as soon 
as the higher, as is evident from Fig. 10, page 70. 


Fig. 10. 

Since light comes to the eye in straight lines, by which 
objects become visible, it is evident, that no reason exists 
why the parts of the ship near the water should not be 
seen as soon as the upper parts. But if the earth be 
a sphere, then the line of sight would pass above the 
deck of the ship, as is represented in Fig. 1 1 ; and as 

the ship drew nearer to land, the lower parts would 
successively rise above this line and come into view ex- 
actly in the manner known to observation. Secondly, 


in a lunar eclipse, which is occasioned by the moon's 
passing through the earth's shadow, the figure of the 
shadow is seen to be spherical, which could not be the 
case unless the earth itself were round. Thirdly, navi- 
gators, by steering continually in one direction, as east 
or west, have in fact come round to the point from 
which they started, and thus confirmed the fact of the 
earth's rotundity beyond all question. One may also 
reach a given place on the earth, by taking directly op- 
posite courses. Thus, he may reach Canton in China, 
by a westerly route around Cape Horn, or by an east- 
erly route around the Cape of Good Hope. All these 
arguments severally prove that the earth is round. 

But I propose, in this Letter, to give you some account 
of the unwearied labors which have been performed to 
ascertain the exact figure of the earth ; for although the 
earth is properly described in general language as round, 
yet it is not an exact sphere. Were it so, all its diam- 
eters would be equal ; but it is known that a diameter 
drawn through the equator exceeds one drawn from 
pole to pole, giving to the earth the form of a spheroid, 
a figure resembling an orange, where the ends are 
flattened a little and" the central parts are swelled out. 

Although it would be a matter of very rational curi- 
osity, to investigate the precise shape of the planet on 
which Heaven has fixed our abode, yet the immense 
pains which has been bestowed on this subject has not 
all arisen from mere curiosity. No accurate measure- 
ments can be taken of the distances and magnitudes 
of the heavenly bodies, nor any exact determinations 
made of their motions, without a knowledge of the ex- 
act figure of the earth ; and hence is derived a power- 
ful motive for ascertaining this element with all possible 

The first satisfactory evidence that was obtained of 
the exact figure of the earth was derived from reason- 
ing on the effects of the earth's centrifugal force, oc- 
casioned by its rapid revolution on its own axis. When 
water is whirled in a pail, we see it recede from the 


centre and accumulate upon the sides of the vessel ; 
and when a millstone is whirled rapidly, since the por- 
tions of the stone furthest from the centre revolve 
much more rapidly than those near to it, their greater 
tendency to recede sometimes makes them fly off with 
a violent explosion. A case, which comes still nearer 
to that of the earth, is exhibited by a mass of clay re- 
volving on a potter's wheel, as seen in the process of 
making earthen vessels. The mass swells out in the 
middle, in consequence of the centrifugal force exerted 
upon it by a rapid motion. Now, in the diurnal revo- 
lution, the equatorial parts of the earth move at the rate 
of about one thousand miles per hour, while the poles 
do not move at all ; and since, as we take points at 
successive distances from the equator towards the pole, 
the rate at which these points move grows constantly 
less and less ; and since, in revolving bodies, the cen- 
trifugal force is proportioned to the velocity, consequent- 
ly, those parts which move with the greatest rapidity 
will be more affected by this force than those which 
move more slowly. Hence, the equatorial regions must 
be higher from the centre than the polar regions ; for, 
were not this the case, the waters on the surface of the 
earth would be thrown towards the equator, and be 
piled up there, just as water is accumulated on the sides 
of a pail when made to revolve rapidly. 

Huyghens, an eminent astronomer of Holland, who 
investigated the laws of centrifugal forces, was the first 
to infer that such must be the actual shape of the earth ; 
but to Sir Isaac Newton we owe the full developement 
of this doctrine. By combining the reasoning derived 
from the known laws of the centrifugal force with argu- 
ments derived from the principles of universal gravita- 
tion, he concluded that the distance through the earth, 
in the direction of the equator, is greater than that in 
the direction of the poles. He estimated the difference 
to be about thirty-four miles. 

But it was soon afterwards determined by the astron- 
omers of France, to ascertain the figure of the earth by 


actual measurements, specially instituted for that pur- 
pose. Let us see how this could be effected. If we 
set out at the equator and travel towards the pole, it is 
easy to see when we have advanced one degree of lat- 
itude, for this will be indicated by the rising of the north 
star, which appears in the horizon when the spectator 
stands on the equator, but rises in the same proportion 
as he recedes from the equator, until, on reaching the 
pole, the north star would be seen directly over head. 
Now, were the earth a perfect sphere, the meridian of 
the earth would be a perfect circle, and the distance be- 
tween any two places, differing one degree in latitude, 
would be exactly equal to the distance between any 
other two places, differing in latitude to the same 
amount. But if the earth be a spheroid, flattened at 
the poles, then a line encompassing the earth from north 
to south, constituting the terrestrial meridian, would not 
be a perfect circle, but an ellipse or oval, having its 
longer diameter through the equator, and its shorter 
through the poles. The part of this curve included 
between two radii, drawn from the centre of the earth 
to the celestial meridian, at angles one degree asunder, 
would be greater in the polar than in the equatorial re- 
gion ; that is, the degrees of the meridian would length- 
en towards the poles. 

The French astronomers, therefore, undertook to as- 
certain by actual measurements of arcs of the meridian, 
in different latitudes, whether the degrees of the merid- 
ian are of uniform length, or, if not, in what manner 
they differ from each other. After several indecisive 
measurements of an arc of the meridian in France, it 
was determined to effect simultaneous measurements of 
arcs of the meridian near the equator, and as near as 
possible to the north pole, presuming that if degrees of 
the meridian, in different latitudes, are really of different 
lengths, they will differ most in points most distant from 
each other. Accordingly, in 1735, the French Acade- 
my, aided by the government, sent out two expeditions, 
one to Peru and the other to Lapland. Three distin- 
7 L. A, 


guished mathematicians, Bouguer, La Condamine, and 
Godin, were despatched to the former place, and four 
others, Maupertius, Camus, Clairault, and Lemonier, 
were sent to the part of Swedisty Lapland which lies at 
the head of the Gulf of Tornea, the northern arm of the 
Baltic. This commission completed its operations sev- 
eral years sooner than the other, which met with great- 
er difficulties in the way of their enterprise. Still, the 
northern detachment had great obstacles to contend 
with, arising particularly from the extreme length and 
severity of their Winters. The measurements, how- 
ever, were conducted with care and skill, and the re- 
sult, when compared with that obtained for the length 
of a degree in France, plainly indicated, by its greater 
amount, a compression of the earth towards the poles. 

Mean-while, Bouguer and his party were prosecuting 
a similar work in Peru, under extraordinary difficulties. 
These were caused, partly by the localities, and partly 
by the ill-will and indolence of the inhabitants. The 
place selected for their operations was in an elevated 
valley between two principal chains of the Andes. The 
lowest point of their arc was at an elevation of a mile 
and a half above the level of the sea ; and, in some in- 
stances, the heights of two neighboring signals differed 
more than a mile. Encamped upon lofty mountains, 
they had to struggle against storms, cold, and privations 
of every description, while the invincible indifference 
of the Indians, they were forced to employ, was not to 
be shaken by the fear of punishment or the hope of re- 
ward. Yet, by patience and ingenuity, they overcame 
all obstacles, and executed with great accuracy one of 
the most important operations, of this nature, ever un- 
dertaken. To accomplish this, however, took them 
nine years ; of which, three were occupied in determin- 
ing the latitudes alone.* 

I have recited the foregoing facts, in order to give you 
some idea of the unwearied pains which astronomers 
have taken to ascertain the exact figure of the earth. 

* Library of Useful Knowledge : History of Astronomy, page 95. 


You will find, indeed, that all their labors are charac- 
terized by the same love of accuracy. Years of toilsome 
watchings, and incredible labor of computation, have 
been undergone, for the sake of arriving only a few sec- 
onds nearer to the trutn. 

The length of a degree of the meridian, as measured 
in Peru, was less than that before determined in France, 
and of course less than that of Lapland ; so that the 
spheroidal figure of the earth appeared now to be ascer- 
tained by actual measurement. Still, these measures 
were too few in number, and covered too small a por- 
tion of the whole quadrant from the equator to the pole, 
to enable astronomers to ascertain the exact law of cur- 
vature of the meridian, and therefore similar measure- 
ments have since been prosecuted with great zeal by 
different nations, particularly by the French and English. 
In 1764, two English mathematicians of great emi- 
nence, Mason and Dixon, undertook the measurement 
of an arc in Pennsylvania, extending more than one 
hundred miles. 

These operations are carried on by what is called a 
system of triangulation. Without some knowledge 
of trigonometry, you will not be able fully to understand 
this process ; but, as it is in its nature somewhat curious, 
and is applied to various other geographical measure- 
ments, as well as to the determination of arcs of the 
meridian, I am desirous that you should understand its 
general principles. Let us reflect, then, that it must 
be a matter of the greatest difficulty, to execute with 
exactness the measurement of a line of any great length 
in one continued direction on the earth's surface. Even 
if we select a level and open country, more or less ine- 
qualities of surface will occur ; rivers must be crossed, 
morasses must be traversed, thickets must be pene- 
trated, and innumerable other obstacles must be sur- 
mounted ; and finally, every time we apply an artificial 
measure, as a rod, for example, we obtain a result not 
absolutely perfect. Each error may indeed be very 
small, but small errors, often repeated, may produce a 


formidable aggregate. Now, one unacquainted with 
trigonometry can easily understand the fact, that, when 
we know certain parts of a triangle, we can find the 
other parts by calculation ; as, in the rule of three in 
arithmetic, we can obtain the fourth term of a propor- 
tion, from having the first three terms given. Thus, in 
the triangle ABC, Fig. 12, if we know the side A B, and 
the angles at A and B, we can find by computation, the 
other sides, A C and B C, and the remaining angle at C. 
Suppose, then, that in measuring an arc of the meridian 
through any country, the line were to pass directly 
Fig. 12. through A B, but the ground was so ob- 
structed between A and B, that we could 
not possibly carry our measurement 
through it. We might then measure 
another line, as A C, which was accessi- 
ble, and with a compass take the bearing 
of B from the points A and C, by which 
means we should learn the value of the 
angles at A and C. From these data we 
A" might calculate, by the rules of trigonom- 

etry, the exact length of the line A B. Perhaps the 
ground might be so situated, that we could not reach the 
point B, by any route ; still, if it could be seen from A 
and C, it would be all we should want. Thus, in con- 
ducting a trigonometrical survey of any country, conspic- 
uous signals are placed on elevated points, and the bear- 
ings of these are taken from the extremities of a known 
line, called the base, and thus the relative situation of 
various places is -accurately determined. Were we to 
undertake to run an exact north and south line through 
any country, as New England, we should select, near 
one extremity, a spot of ground favorable for actual 
measurement, as a level, unobstructed plain ; we should 
provide a measure whose length in feet and inches was 
determined with the greatest possible precision, and 
should apply it with the utmost care. We should thus 
obtain a base line. From the extremities of this line, 
we should take (with some appropriate instrument) the 



bearing of some signal at a greater or less distance, and 
thus we should obtain one side and two angles of a tri- 
angle, from which we could find, by the rules of trigo- 
nometry, either of the unknown sides. Taking this as 
a new base, we might take the bearing of another sig- 
nal, still further on our way, and thus proceed to run 
the required north and south line, without actually 
measuring any thing more than the first, or base line. 
Thus, in Fig. 13, we wish to measure the distance be- 
tween the two points A and O, which are both on the 
same meridian, as is known by their having the same 
longitude ; but, on account of Fig. 13. 

various obstacles, it would be 
found very inconvenient to mea- 
sure this line directly, with a rod 
or chain, and even if we could do 
it, we could not by this method 
obtain nearly so accurate a re- 
sult, as we could by a series of 
triangles, where, after the base 
line was measured, we should 
have nothing else to measure ex- 
cept angles, which can be de- 
termined, by observation, to a 
greater degree of exactness, than 
lines. We therefore, in the first 
place, measure the base line, A B, 
with the utmost precision. Then, 
taking the bearing of some sig- 
nal at C from A and B, we ob- 
tain the means of calculating the side B C, as has been 
already explained. Taking B C as a new base, we pro- 
ceed, in like manner, to determine successively the sides 
C D, D E, and E F, and also A C, and C E. Although 
A C is not in the direction of the meridian, but consid- 
erably to the east of it, yet it is easy to find the cor- 
responding distance on the meridian, A M ; and in the 
same manner we can find the portions of the meridian 
M N and N O, corresponding respectively to C E and 


E F. Adding these several parts of the meridian to- 
gether, we obtain the length of the arc from A to O, in 
miles ; and by observations on the north star, at each 
extremity of the arc, namely, at A and at O, we could 
determine the difference of latitude between these two 
points. Suppose, for example, that the distance be- 
tween A and O is exactly five degrees, and that the 
length of the intervening line is three hundred and for- 
ty-seven miles ; then, dividing the latter by the former 
number, we find the length of a degree to be sixty- 
nine miles and four tenths. To take, however, a few 
of the results actually obtained, they are as follows : 


Places of observation. Latitude. in mileg 

Peru, 00 00' 00" 68.732 

Pennsylvania, .... 39 12 00 68.896 

France, 46 12 00 69.054 

England, 51 29 54J 69.146 

Sweden, 66 20 10 69.292 

This comparison shows, that the length of a degree 
gradually increases, as we proceed from the equator 
towards the pole. Combining the results of various 
estimates, the dimensions of the terrestrial spheroid are 
found to be as follows : 

Equatorial diameter, .... 7925.648 miles. 

Polar diameter, 7899.170 " 

Average diameter, 7912.409 " 

The difference between the greatest and the least is 
about twenty-six and one half miles, which is about one 
two hundred and ninety-ninth part of the greatest. 
This fraction is denominated the ellipticity of the earth, 
being the excess of the equatorial over the polar di- 

The operations, undertaken for the purpose of deter- 
mining the figure of the earth, have been conducted 
with the most refined exactness. At any stage of the 
process, the length of the last side, as obtained by cal- 
culation, may be actually measured in the same manner 


as the base from which the series of triangles commenc- 
ed. When thus measured, it is called the base of veri- 
fication. In some surveys, the base of verification, 
when taken at a distance of four hundred miles from 
the starting point, has not differed more than one foot 
from the same line, as determined by calculation. 

Another method of arriving at the exact figure of the 
earth is, by observations with the pendulum. If a pen- 
dulum, like that of a clock, be suspended, and the num- 
ber of its vibrations per hour be counted, they will be 
found to be different in different latitudes. A pendulum 
that vibrates thirty-six hundred times per hour, at the 
equator, will vibrate thirty-six hundred and five and two 
thirds times, at London, and a still greater number of 
times nearer the north pole. Now, the vibrations of the 
pendulum are produced by the force of gravity. Hence 
their comparative number at different places is a meas- 
ure of the relative forces of gravity at those places. But 
when we know the relative forces of gravity at different 
places, we know their relative distances from the centre 
of the earth ; because the nearer a place fs to the centre 
of the earth, the greater is the force of gravity. Sup- 
pose, for example, we should count the number of vi- 
brations of a pendulum at the equator, and then carry 
it to the north pole, and count the number of vibrations 
made there in the same time, we should be able, from 
these two observations, to estimate the relative forces 
of gravity at these two points ; and, having the relative 
forces of gravity, we can thence deduce their relative 
distances from the centre of the earth, and thus obtain 
the polar and equatorial diameters. Observations of 
this kind have been taken with the greatest accuracy, 
in many places on the surface of the earth, at various 
distances from each other, and they lead to the same 
conclusions respecting the figure of the earth, as those 
derived from measuring arcs of the meridian. It is 
pleasing thus to see a great truth, and one apparently 
beyond the pale of human investigation, reached by two 
routes entirely independent of each other. Nor, in- 


deed, are these the only proofs which have been dis- 
covered of the spheroidal figure of the earth. In con- 
sequence of the accumulation of matter above the equa- 
torial regions of the earth, a body weighs less there than 
towards the poles, being further removed from the cen- 
tre of the earth. The same accumulation of matter, 
by the force of attraction which it exerts, causes slight 
inequalities in the motions of the moon ; and since the 
amount of these becomes a measure of the force which 
produces them, astronomers are able, from these in- 
equalities, to calculate the exact quantity of the matter 
thus accumulated, and hence to determine the figure 
of the earth. The result is not essentially different from 
that obtained by the other methods. Finally, the shape 
of the earth's shadow is altered, by its spheroidal figure, 
a circumstance which affects the time and duration of 
a lunar eclipse. All these different and independent 
phenomena afford a pleasing example of the harmony 
of truth. The known effects of the centrifugal force 
upon a body revolving on its axis, like the earth, lead 
us to infer that the earth is of a spheroidal figure ; but 
if this be the fact, the pendulum ought to vibrate faster 
near the pole than at the equator, because it would 
there be nearer the centre of the earth. On trial, such 
is found to be the case. If, again, there be such an 
accumulation of matter about the equatorial regions, its 
effects ought to be visible in the motions of the moon, 
which it would influence by its gravity ; and there, also, 
its effects are traced. At length, we apply our meas- 
ures to the surface of the earth itself, and find the same 
fact, which had thus been searched out among the hid- 
den things of Nature, here palpably exhibited before 
our eyes. Finally, on estimating from these different 
sources, what the exact amount of the compression at 
the poles must be, all bring out nearly one and the 
same result. This truth, so harmonious in itself, takes 
along with it, and establishes, a thousand other truths 
on which it rests. 




' To some she taught the fabric of the sphere, 
The changeful moon, the circuit of the stars, 
The golden zones of heaven." Akenside. 

WITH the elementary knowledge already acquired, 
you will now be able to enter with pleasure and profit 
on the various interesting phenomena dependent on the 
revolution of the earth on its axis and around the sun. 
The apparent diurnal revolution of the heavenly bod- 
ies, from east to west, is owing to the actual revolution 
of the earth on its own axis, from west to east. If we 
conceive of a radius of the earth's equator extended 
until it meets the concave sphere of the heavens, then, 
as the earth revolves, the extremity of this line would 
trace out a curve on the face of the sky ; namely, the 
celestial equator. In curves parallel to this, called the 
circles of diurnal revolution, the heavenly bodies act- 
ually appear to move, every star having its own pecu- 
liar circle. After you have first rendered familiar the 
real motion of the earth from west to east, you may 
then, without danger of misapprehension, adopt the 
common language, that all the heavenly bodies revolve 
around the earth once a day, from east to west, in cir- 
cles parallel to the equator and to each other. 

I must remind you, that the time occupied by a star, 
in passing from any point in the meridian until it comes 
round to the same point again, is called a sidereal day, 
and measures the period of the earth's revolution on its 
axis. If we watch the returns of the same star from 
day to day, we shall find the intervals exactly equal to 
each other ; that is, the sidereal days are all equal. 
Whatever star we select for the observation, the same 
result will be obtained. The stars, therefore, always 
keep the same relative position, and have a common 


movement round the earth, a consequence that natu- 
rally flows from the hypothesis that their apparent mo- 
tion is all produced by a single real motion : namely, that 
of the earth. The sun, moon, and planets, as well as 
the fixed stars, revolve in like manner ; but their returns 
to the meridian are not, like those of the fixed stars, 
at exactly equal intervals. 

The appearances of the diurnal motions of the heav- 
enly bodies are different in different parts of the earth, 
since every place has its own horizon, and different 
horizons are variously inclined to each other. Noth- 
ing in astronomy is more apt to mislead us, than the 
obstinate habit of considering the horizon as a fixed 
and immutable plane, and of referring every thing to it. 
We should contemplate the earth as a huge globe, oc- 
cupying a small portion of space, and encircled on all 
sides, at an immense distance, by the starry sphere. We 
should free our minds from their habitual proneness to 
consider one part of space as naturally up and another 
down, and view ourselves as subject to a force (gravity) 
which binds us to the earth as truly as though we were 
fastened to it by some invisible cords or wires, as the 
needle attaches itself to all sides of a spherical load- 
stone. We should dwell on this point, until it appears 
to us as truly up, in the direction B B, C C, D D, when 
one is at B, C, D, respectively, as in the direction A A, 
when he is at A, Fig. 14. 

Let us now suppose the spectator viewing the diur- 
nal revolutions from several different positions on the 
earth. On the equator, his horizon would pass through 
both poles ; for the horizon cuts the celestial vault at 
ninety degrees in every direction from the zenith of the 
spectator ; but the pole is likewise ninety degrees from 
his zenith, when he stands on the equator ; and conse- 
quently, the pole must be in the horizon. Here, also, the 
celestial equator would coincide with the prime vertical, 
being a great circle passing through the east and west 
points. Since all the diurnal circles are parallel to the 
equator, consequently, they would all, like the equator, 


Fiff. 14. 

be perpendicular to the horizon. Such a view of the 
heavenly bodies is called a right sphere, which may be 
thus defined : a right sphere is one in which all the 
daily revolutions of the stars are in circles perpendic- 
ular to the horizon. 

A right sphere is seen only at the equator. Any 
star situated in the celestial equator would appear to rise 
directly in the east, at midnight to be in the zenith of 
the spectator, and to set directly in the west. In pro- 
portion as stars are at a greater distance from the equa- 
tor fto wards the pole, they describe smaller and smaller 
circles, until, near the pole, their motion is hardly per- 

If the spectator advances one degree from the equa- 
tor towards the north pole, his horizon reaches one de- 
gree beyond the pole of the earth, and cuts the starry 
sphere one degree below the pole of the heavens, or 
below the north star, if that be taken as the place of 
the pole. As he moves onward towards the pole, his 
horizon continually reaches further and further beyond 
it, until, when he comes to the pole of the earth, and 
under the pole of the heavens, his horizon reaches on 
all sides to the equator, and coincides with it. More- 


over, since all the circles of daily motion are parallel to 
the equator, they become, to the spectator at the pole, 
parallel to the horizon. Or, a parallel sphere is that 
in which all the circles of daily motion are parallel to 
the horizon. 

To render this view of the heavens familiar, I would 
advise you to follow round in mind a number of separ- 
ate stars, in their diurnal revolution, one near the hori- 
zon, one a few degrees above it, and a third near the 
zenith. To one who stood upon the north pole, the 
stars of the northern hemisphere would all be perpet- 
ually in view when not obscured by clouds, or lost in the 
sun's light, and none of those of the southern hemis- 
phere would ever be seen. The sun would be con- 
stantly above the horizon for six months in the year, and 
the remaining six continually out of sight. That is, at 
the pole, the days and nights are each six months long. 
The appearances at the south pole are similar to those 
at the north. 

A perfect parallel sphere can never be seen, except 
at one of the poles, a point which has never been ac- 
tually reached by man ; yet the British discovery ships 
penetrated within a few degrees of the north pole, and 
of course enjoyed the view of a sphere nearly parallel. 

As the circles of daily motion are parallel to the hori- 
zon of the pole, and perpendicular to that of the equa- 
tor, so at all places between the two, the diurnal mo- 
tions are oblique to the horizon. This aspect of the 
heavens constitutes an oblique sphere, which is thus 
defined : an oblique sphere is that in which the circles 
of daily motion are oblique to the horizon. 

Suppose, for example, that the spectator is at the 
latitude of fifty degrees. His horizon reaches fifty de- 
grees beyond the pole of the earth, and gives the same 
apparent elevation to the pole of the heavens. It cuts 
the equator and all the circles of daily motion, at an 
angle of forty degrees, being always equal to what the 
altitude of the pole lacks of ninety degrees ; that is, it 
is always equal to the co-altitude of the pole. Thus, 



Fig. 15. 

let H O, Fig. 15, represent the horizon, E Q, the equa- 
tor, and P P' the axis of 
the earth. Also, I Z, m 
w, n w, parallels of lat- 
itude. Then the hori- 
zon of a spectator at Z, 
in latitude fifty degrees, 
reaches to fifty degrees 
beyond the pole ; and 
the angle E C H, which 
the equator makes with 
the horizon, is forty 
degrees, the comple- 
ment of the latitude. 
As we advance still fur- 
ther north, the elevation of the diurnal circle above 
the horizon grows less and less, and consequently, the 
motions of the heavenly bodies more and more oblique 
to the horizon, until finally, at the pole, where the lati- 
tude is ninety degrees, the angle of elevation of the 
equator vanishes, and the horizon and the equator co- 
incide with each other, as before stated. 

The circle of perpetual apparition is the boundary 
of that space around the elevated pole, where the stars 
never set. Its distance from the pole is equal to the 
latitude of the place. For, since the altitude of the 
pole is equal to the latitude, a star, whose polar distance 
is just equal to the latitude, will, when at its lowest 
point, only just reach the horizon ; and all the stars 
nearer the pole than this will evidently not descend so 
far as the horizon. Thus m m, Fig. 15, is the circle of 
perpetual apparition, between which and the north 
pole, the stars never set, and its distance from the 
pole, O P, is evidently equal to the elevation of the 
pole, and of course to the latitude. 

In the opposite hemisphere, a similar part of the 
sphere adjacent to the depressed pole never rises. 
Hence, the circle of perpetual occultation is the boun- 

8 L. A. 


dary of that space around the depressed pole, within 
which the stars never rise. 

Thus m m', Fig. 15, is the circle of perpetual occul- 
tation, between which and the south pole, the stars 
never rise. 

In an oblique sphere, the horizon cuts the circles of 
daily motion unequally. Towards the elevated pole, 
more than half the circle is above the horizon, and a 
greater and greater portion, as the distance from the 
equator is increased, until finally, within the circle of 
perpetual apparition, the whole circle is above the ho- 
rizon. Just the opposite takes place in the hemisphere 
next the depressed pole. Accordingly, when the sun 
is in the equator, as the equator and horizon, like all 
other great circles of the sphere, bisect each other, the 
days and nights are equal all over the globe. But 
when the sun is north of the equator, the days become 
longer than the nights, but shorter, when the sun is 
south of the equator. Moreover, the higher the lati- 
tude, the greater is the inequality in the lengths of the 
days and nights. By examining Fig. 15, you will easi- 
ly see how each of these cases must hold good. 

Most of the appearances of the diurnal revolution 
can be explained, either on the supposition that the ce- 
lestial sphere actually turns around the earth once in 
twenty-four hours, or that this motion of the heavens 
is merely apparent, arising from the revolution of the 
earth on its axis, in the opposite direction, a mo- 
tion of which we are insensible, as we sometimes lose 
the consciousness of our own motion in a ship or steam- 
boat, and observe all external objects to be receding 
from us, with a common motion. Proofs, entirely con- 
clusive and satisfactory, establish the fact, that it is the 
earth, and not the celestial sphere, that turns ; but these 
proofs are drawn from various sources, and one is not 
prepared to appreciate their value, or even to under- 
stand some of them, until he has made considerable 
proficiency in the study of astronomy, and become fa- 
miliar with a great variety of astronomical phenomena. 


To such a period we will therefore postpone the dis- 
cussion of the earth's rotation on its axis. 

While we retain the same place on the earth, the 
diurnal revolution occasions no change in our horizon, 
but our horizon goes round, as well as ourselves. Let 
us first take our station on the equator, at sunrise ; our 
horizon now passes through both the poles and through 
the sun, which we are to conceive of as at a great dis- 
tance from the earth, and therefore as cut, not by the 
terrestrial, but by the celestial, horizon. As the earth 
turns, the horizon dips more and more below the sun, 
at the rate of fifteen degrees for every hour ; and, as 
in the case of the polar star, the sun appears to rise at 
the same rate. In six hours, therefore, it is depressed 
ninety degrees below the sun, bringing us directly un- 
der the sun, which, for our present purpose, we may 
consider as having all the while maintained the same 
fixed position in space. The earth continues to turn, 
and in six hours more, it completely "reverses the posi- 
tion of our horizon, so that the western part of the ho- 
rizon, which at sunrise was diametrically opposite to the 
sun, now cuts the sun, and soon afterwards it rises 
above the level of the sun, and the sun sets. During 
the next twelve hours, the sun continues on the invisible 
side of the sphere, until the horizon returns to the po- 
sition from which it set out, and a new day begins. 

Let us next contemplate the similar phenomena at 
the poles. Here the horizon, coinciding, as it does, 
with the equator, would cut the sun through its centre 
and the sun would appear to revolve along the surface 
of the sea, one half above and the other half below the 
horizon. This supposes the sun in its annual revolution 
to be at one of the equinoxes. When the sun is north 
of the equator, it revolves continually round in a circle, 
which, during a single revolution, appears parallel to 
the equator, and it is constantly day ; and when the 
sun is south of the equator, it is, for the same reason, 
continual night. 

When we have gained a clear idea of the appear- 


ances of the diurnal revolutions, as exhibited to a spec- 
tator at the equator and at the pole, that is, in a right 
and in a parallel sphere, there will be little difficulty in 
imagining how they must be in the intermediate lati- 
tudes, which have an oblique sphere. 

The appearances of the sun and stars, presented to 
the inhabitants of different countries, are such as cor- 
respond to the sphere in which they live. Thus, in the 
fervid climates of India, Africa, and South America, the 
sun mounts up to the highest regions of the heavens, 
and descends directly downwards, suddenly plunging 
beneath the horizon. His rays, darting almost vertically 
upon the heads of the inhabitants, strike with a force 
unknown to the people of the colder climates ; while in 
places remote from the equator, as in the north of Eu- 
rope, the sun, in Summer, rises very far in the north, 
takes a long circuit towards the south, and sets as far 
northward in the west as the point where it rose on 
the other side of the meridian. As we go still further 
north, to the northern parts of Norway and Sweden, for 
example, to the confines of the frigid zone, the Sum- 
mer's sun just grazes the northern horizon, and at noon 
appears only twenty-three and one half degrees above 
the southern. On the other hand, in midwinter, in 
the north of Europe, as at St. Petersburgh, the day 
dwindles almost to nothing, lasting only while the sun 
describes a very short arc in the extreme south. In 
some parts of Siberia and Iceland, the only day consists 
of a little glimmering of the sun on the verge of the 
southern horizon, at noon. 




u Go, wondrous creature ! mount where science guides, 
Go measure earth, weigh air, and state the tides ; 
Instruct the planets in what orbs to run, 
Correct old Time, and regulate the sun." Pope. 

I THINK you must have felt some astonishment, that 
astronomers are able to calculate the exact distances 
and magnitudes of the sun, moon, and planets. We 
should, at the first thought, imagine that such knowl- 
edge as this must be beyond the reach of the human 
faculties, and we might be inclined to suspect that as- 
tronomers practise some deception in this matter, for 
the purpose of exciting the admiration of the unlearn- 
ed. I will therefore, in the present Letter, endeav- 
or to give you some clear and correct views respecting 
the manner in which astronomers acquire this knowl- 

In our childhood, we all probably adopt the notion 
that the sky is a real dome of definite surface, in which 
the heavenly bodies are fixed. When any objects are 
beyond a certain distance from the eye, we lose all 
power of distinguishing, by our sight alone, between 
different distances, and cannot tell whether a given ob- 
ject is one million or a thousand millions of miles off. 
Although the bodies seen in the sky are in fact at dis- 
tances extremely various, some, as the clouds, only a 
few miles off; others, as the moon, but a few thousand 
miles ; and others, as the fixed stars, innumerable mil- 
lions of miles from us, yet, as our eye cannot distin- 
guish these different distances, we acquire the habit of 
referring all objects beyond a moderate height to one 
and the same surface, namely, an imaginary spherical 
surface, denominated the celestial vault. Thus, the va- 
rious objects represented in the diagram on next page, 
though differing very much in shape and diameter, 


would all be projected upon the sky alike, and com- 
pose a part, indeed, of the imaginary vault itself. The 
place which each object occupies is determined by 
lines drawn from the eye of the spectator through the 
extremities of the body, to meet the imaginary concave 
sphere. Thus, to a spectator at O, Fig 16, the several 
lines A B, C D, and E F, would all be projected into 

Fig. 16. 


arches on the face of the sky, and be seen as parts of 
the sky itself, as represented by the lines A' B', C' D', 
and E' F'. And were a body actually to move in the 
several directions indicated by these lines, they would 
appear to the spectator to describe portions of the ce- 
lestial vault. Thus, even when moving through the 
crooked line, from a to 6, a body would appear to be 
moving along the face of the sky, and of course in a 
regular curve line, from c to d. 

But, although all objects, beyond a certain moderate 
height, are projected on the imaginary surface of the 
sky, yet different spectators will project the same ob- 
ject on different parts of the sky. Thus, a spectator 
at A, Fig. 17, would see a body, C, at M, while a spec- 
tator at B would see the same body at N. This change 
of place in a body, as seen from different points, is called 
parallax, which is thus defined : parallax is the ap- 
parent change of place which bodies undergo by being 
viewed from different points. 


The arc M N is called the parallactic arc, and the 
angle A C B, the parallactic angle. 

It is plain, from the figure, that near objects are much 
more affected by parallax than distant ones. Thus, the 
body C, Fig. 17, makes a much greater parallax than the 
more distant body D, the former being measured by 
the arc M N, and the latter by the arc O P. We may 
easily imagine bodies to be so distant, that they would 
appear projected at very nearly the same point of the 
heavens, when viewed from places very remote from 
each other. Indeed, the fixed stars, as we shall see 
more fully hereafter, are so distant, that spectators, a 
hundred millions of miles apart, see each star in one 
and the same place in the heavens. 

It is by means of parallax, that astronomers find the 
distances and magnitudes of the heavenly bodies. In 
order fully to understand this subject, one requires to 
know something of trigonometry, which science ena- 
bles us to find certain unknown parts of a triangle from 
certain other parts which are known. Although you 
may not be acquainted with the principles of trigo- 
nometry, yet you will readily understand, from your 
knowledge of arithmetic, that from certain things given 
in a problem others may be found. Every triangle has 
of course three sides and three angles ; and, if we know 


Fi g. is. 

two of the angles and one of the sides, we can find all 
the other parts, namely, the remaining angle and the 
two unknown sides. Thus, in the triangle ABC, 
Fig. 18, if we know the length of the side A B, and 

how many degrees each 
i of the angles ABC and 
B C A contains, we can 
find the length of the 
side B C, or of the side 
A C, and the remaining 
angle at A. Now, let 
us apply these principles 
to the measurements of 
some of the heavenly bodies. 

In Fig. 19, let A represent the earth, C H the hori- 
zon, and H Z a quadrant of a great circle of the heav- 

Fig. 19. 

ens, extending from the horizon to the zenith ; and 
let E, F, G, O, be successive positions of the moon, at 
different elevations, from the horizon to the meridian. 
Now, a spectator on the surface of the earth, at A, would 


refer the moon, when at E, to h, on the face of the sky, 
whereas, if seen from the centre of the earth, it would 
appear at H. So, when the moon was at F, a specta- 
tor at A would see it at p, while, if seen from the cen- 
tre, it would have appeared at P. The parallactic arcs, 
H h, P p, R r, grow continually smaller and smaller, as 
a body is situated higher above the horizon ; and when 
the body is in the zenith, then the parallax vanishes al- 
together, for at O the moon would be seen at Z, wheth- 
er viewed from A or C. 

Since, then, a heavenly body is liable to be referred 
to different points on the celestial vault, when seen 
from different parts of the eaVth, and thus some confu- 
sion be occasioned in the determination of points on the 
celestial sphere, astronomers have agreed to consider 
the true place of a celestial object to be that where it 
would appear, if seen from the centre of the earth ; and 
the doctrine of parallax teaches how to reduce observa- 
tions made at any place on the surface of the earth, to 
such as they would be, if made from the centre. 

When the moon, or any heavenly body, is seen in the 
horizon, as at E, the change of place is called the hori- 
zontal parallax. Thus, the angle A E C, measures the 
horizontal parallax of the moon. Were a spectator to 
view the earth from the centre of the moon, he would 
see the semidiameter of the earth under this same an- 
gle ; hence, the horizontal parallax of any body is the 
angle subtended by the semidiameter of the earth, as 
seen from the body. Please to remember this fact. 

It is evident from the figure, that the effect of paral- 
lax upon the place of a celestial body is to depress it. 
Thus, in consequence of parallax, E is depressed by the 
arc H h ; F, by the arc P p ; G, by the arc R r ; while 
O sustains no change. Hence, in all calculations re- 
specting the altitude of the sun, moon, or planets, the 
amount of parallax is to be added : the stars, as we 
shall see hereafter, have no sensible parallax. 

It is now very easy to see how, when the parallax 
of a body is known, we may find its distance from the 



Fig. 20. 

centre of the earth. Thus, in the triangle ACE, 
Fig. 19, the side A C is known, being the semidi- 
ameter of the earth ; the angle C A E, being a right 
angle, is also known ; and the parallactic angle, A E C, 
is found from observation ; and it is a wellknown prin- 
ciple of trigonometry, that when we have any two an- 
gles of a triangle, we may find the remaining angle by 
subtracting the sum of these two from one hundred and 
eighty degrees. Consequently, in the triangle A E C, 
we know all the angles and one side, namely, the side 
A C ; hence, we have the means of finding the side 
C E, which is the distance from the centre of the earth 
to the centre of the moon. 

When the distance of a heavenly 
^ *y t is known, and we can measure, 
^ ^instruments, its angular breadth, 
s jcan easily determine its magni- 
tude. Thus, if we have the distance 
of the moon, E S, Fig. 20, and half 
the breadth of its disk S C, (which is 
measured by the angle S E C,)we can 
find the length of the line, S C, in 
miles. Twice this line is the diame- 
ter of the body ; and when we know 
the diameter of a sphere, we can, by 
wellknown rules, find the contents 
qf the surface, and its solidity. 

You will perhaps be curious to 
know, how the moon's horizontal parallax is found ; 
for it must have been previously ascertained, before we 
could apply this method to finding the distance of the 
moon Jrom the earth. Suppose that two astronomers 
take their stations on the same meridian, but one south 
of the equator, as at the Cape of Good Hope, and an- 
other north of the equator, as at Berlin, in Prussia, which 
two places lie nearly on the same meridian. The ob- 
servers would severally refer the moon to different 
points on the face of the sky, the southern observer 
carrying it further north, and the northern observer fur- 



ther south, than its true place, 
as seen from the centre of the 
earth. This will be plain from 
the diagram, Fig. 21. If A 
and B represent the positions 
of the spectators, M the moon, 
and C D an arc of the sky, 
then it is evident, that C D 
would be the parallactic arc. 

These observations furnish 
materials for calculating, by 
the aid of trigonometry, the 
moon's horizontal parallax, 
and we have before seen how, 
when we know the parallax of a h^ < s ph-body, we can 
find both its distance from the can i.' e Pt ts magnitude. 

Beside the change of place wh. chese heavenly 
bodies undergo, in consequence of parallax, there is 
another, of an opposite kind, arising from the effect of 
the atmosphere, called refraction. Refraction elevates 
the apparent place of a body, while parallax depresses 
it. It affects alike the most distant as well as nearer 

In order to understand the nature of refraction, we 
must consider, that an object always appears in the di- 
rection in which the last ray of light comes to the eye. 
If the light which comes from a star were bent into fifty 
directions before it reached the eye, the star would nev- 
ertheless appear in the line described by the ray nearest 
the eye. The operation of this principle is seen when 
an oar, or any stick, is thrust into water. As the rays 
of light by which the oar is seen have their direction 
changed as they pass out of water into air, the apparent 
direction in wjfiich the body is seen is changed in the 
same degree, giving it a bent appearance, the part be- 
low the water having apparently a different direction 
from the part above. Thus, in Fig. 22, page 96, if 
S a x be the oar, S a b will be the bent appearance, 
as affected by refraction. Thb transparent substance 


Fig. 22. 

through whi ^ any ray of light passes is called a medi- 
um. It is a >eral fact in optics, that, when light 
passes out of a i , rer into a denser medium, as out of 
air into water, or out of space into air, it is turned 
towards a perpendicular to the surface of the medium ; 
and when it passes out of a denser into a rarer medi- 
um, as out of water into air, it is turned from the per- 
pendicular. In the above case, the light, passing out 
of space into air, is turned towards the radius of the 
earth, this being perpendicular to the surface of the at- 
mosphere ; and it is turned more and more towards 
that radius the nearer it approaches to the earth, be- 
cause the density of the air rapidly increases near the 

Let us now conceive of the atmosphere as made up 
of a great number of parallel strata, as A A, B B, C C, 
and D D, increasing rapidly in density (as is known to 
be the fact) in approaching near to the surface of the 
earth. Let S be a star, from which a ray of light, S a, 
enters the atmosphere at a, where, being much turned 
towards the radius of the convex surface, it would 
change its direction into the line a b, and again into 
b c, and c O, reaching the eye at O. Now, since an 
object always appears in the direction in which the 
light finally strikes the eye, the star would be seen in 
the direction O c, and, consequently, the star would 


apparently change its place, by refraction, from S to S', 
being elevated out of its true position. Moreover, since, 
on account of the continual increase of density in de- 
scending through the atmosphere, the light would be 
continually turned out of its course more and more, it 
would therefore move, not in the polygon represented in 
the figure, but in a corresponding curve line, whose cur- 
vature is rapidly increased near the surface of the earth. 

When a body is in the zenith, since a ray of light 
from it enters the atmosphere at right angles to the re- 
fracting medium, it suffers no refraction. Consequent- 
ly, the position of the heavenly bodies, when in the 
zenith, is not changed by refraction, while, near the 
horizon, where a ray of light strikes the medium very 
obliquely, and traverses the atmosphere through its 
densest part, the refraction is greatest. The whole 
amount of refraction, when a body is in the horizon, is 
thirty-four minutes ; while, at only an elevation of one 
degree, the refraction is but twenty-four minutes ; and at 
forty-five degrees, it is scarcely a single minute. Hence 
it is always important to make our observations on the 
heavenly bodies when they are at as great an elevation 
as possible above the horizon, being then less affected 
by refraction than at lower altitudes. 

Since the whole amount of refraction near the horizon 
exceeds thirty-three minutes, and the diameters of the 
sun and moon are severally less than this, these lumina- 
ries are in view both before they have actually risen and 
after they have set. 

The rapid increase of refraction near the horizon is 
strikingly evinced by the oval figure which the sun as- 
sumes when near the horizon, and which is seen to the 
greatest advantage when light clouds enable us to view 
the solar disk. Were all parts of the sun equally raised 
by refraction, there would be no change of figure ; but, 
since the lower side is more refracted than the upper, the 
effect is to shorten the vertical diameter, and thus to 
give the disk an oval form. This effect is particularly 
remarkable when the sun, at his rising or setting, is ob- 

9 L. A. 


served from the top of a mountain, or at an elevation 
near the seashore ; for in such situations, the rays of 
light make a greater angle than ordinary with a perpen- 
dicular to the refracting medium, and the amount of 
refraction is proportionally greater. In some cases of 
this kind, the shortening of the vertical diameter of the 
sun has been observed to amount to six minutes, or 
about one fifth of the whole. 

The apparent enlargement of the sun and moon, 
when near the horizon, arises from an optical illusion. 
These bodies, in fact, are not seen under so great an 
angle when in the horizon as when on the meridian, for 
they are nearer to us in the latter case than in the for- 
mer. The distance of the sun, indeed, is so great, that 
it makes very little difference in his apparent diameter 
whether he is viewed in the horizon or on the meridi- 
an ; but with the moon, the case is otherwise ; its angu- 
lar diameter, when measured with instruments, is per- 
ceptibly larger when at its culmination, or highest ele- 
vation above the horizon. Why, then, do the sun and 
moon appear so much larger when near the horizon ? 
It is owing to a habit of the mind, by which we judge 
of the magnitudes of distant objects, not merely by the 
angle they subtend at the eye, but also by our impres- 
sions respecting their distance, allowing, under a given 
angle, a greater magnitude as we imagine the distance 
of a body to be greater. Now, on account of the nu- 
merous objects usually in sight between us and the sun, 
when he is near the horizon, he appears much further 
removed from us than when on the meridian ; and we 
unconsciously assign to him a proportionally greater 
magnitude. If we view the sun, in the two positions, 
through a smoked glass, no such difference of size is 
observed ; for here no objects are seen but the sun him- 

Twilight is another phenomenon depending on the 
agency of the earth's atmosphere. It is that illumina- 
tion of the sky which takes place just before sunrise, 
and which continues after sunset. It is owing partly 


to refraction, and partly to reflection, but mostly to the 
latter. While the sun is within eighteen degrees of the 
horizon, before it rises or after it sets, some portion of 
its light is conveyed to us, by means of numerous re- 
flections from the atmosphere. At the equator, where 
the circles of daily motion are perpendicular to the ho- 
rizon, the sun descends through eighteen degrees in an 
hour and twelve minutes. The light of day, therefore, 
declines rapidly, and as rapidly advances after daybreak 
in the morning. At the pole, a constant twilight is 
enjoyed while the sun is within eighteen degrees of the 
horizon, occupying nearly two thirds of the half year 
when the direct light of the sun is withdrawn, so that 
the progress from continual day to constant night is 
exceedingly gradual. To an inhabitant of an oblique 
sphere, the twilight is longer in proportion as the place 
is nearer the elevated pole. 

Were it not for the power the atmosphere has of 
dispersing the solar light, and scattering it in various 
directions, no objects would be visible to us out of di- 
rect sunshine ; every shadow of a passing cloud would 
involve us in midnight darkness ; the stars would be 
visible all day ; and every apartment into which the sun 
had not direct admission would be involved in the ob- 
scurity of night. This scattering action of the atmos- 
phere on the solar light is greatly increased by the ir- 
regularity of temperature caused by the sun, which 
throws the atmosphere into a constant state of undula- 
tion ; and by thus bringing together masses of air of 
different temperatures, produces partial reflections and 
refractions at their common boundaries, by which means 
much light is turned aside from a direct course, and di- 
verted to the purposes of general illumination.* In the 
upper regions of the atmosphere, as on the tops of very 
high mountains, where the air is too much rarefied to 
reflect much light, the sky assumes a black appearance, 
and stars become visible in the day time. 

Although the atmosphere is usually so transparent, 

* Sir J. Herschel. 


that it is invisible to us, yet we as truly move and live 
in a fluid as fishes that swim in the sea. Considered in 
comparison with the whole earth, the atmosphere is to 
be regarded as a thin layer investing the surface, like 
a film of water covering the surface of an orange. Its 
actual height, however, is over a hundred miles, though 
we cannot assign its precise boundaries. Being per- 
fectly elastic, the lower portions, bearing as they do, 
the weight of all the mass above them, are greatly 
compressed, while the upper portions having little to 
oppose the natural tendency of air to expand, diffuse 
themselves widely. The consequence is, that the at- 
mosphere undergoes a rapid diminution of density, as 
we ascend from the earth, and soon becomes exceed- 
ingly rare. At so moderate a height as seven miles, it 
is four times rarer than at the surface, and continues to 
grow rare in the same proportion, namely, being four 
times less for every seven miles of ascent. It is only, 
therefore, within a few miles of the earth, that the at- 
mosphere is sufficiently dense to sustain clouds and va- 
pors, which seldom rise so high as eight miles, and are 
usually much nearer to the earth than this. So rare 
does the air become on the top of Mount Chimborazo, 
in South America, that it is incompetent to support 
most of the birds that fly near the level of the sea. 
The condor, a bird which has remarkably long wings, 
and a light body, is the only bird seen towering above 
this lofty summit. The transparency of the atmos- 
phere, a quality so essential to fine views of the starry 
heavens, is much increased by containing a large pro- 
portion of water, provided it is perfectly dissolved, or in 
a state of invisible vapor. A country at once hot and 
humid, like some portions of the torrid zone, presents a 
much brighter and more beautiful view of the moon 
and stars, than is seen in cold climates. Before a co- 
pious rain, especially in hot weather, when the atmos- 
phere is unusually humid, we sometimes observe the sky 
to be remarkably resplendent, even in our own latitude. 
Accordingly, this unusual clearness of the sky, when 

THE SUN. 101 

the stars shine with unwonted brilliancy, is regarded as 
a sign of approaching rain ; and when, after the rain 
is apparently over, the air is remarkably transparent, 
and distant objects on the earth are seen with uncom- 
mon distinctness, while the sky exhibits an unusually 
deep azure, we may conclude that the serenity is only 
temporary, and that the rain will probably soon return. 



" Great source of day ! best image here below 
Of thy Creator, ever pouring wide, 
From world to world, the vital ocean round, 
On Nature write, with every beam, His praise." Thomson. 

THE subjects which have occupied the preceding 
Letters are by no means the most interesting parts of 
our science. They constitute, indeed, little more than 
an introduction to our main subject, but comprise such 
matters as are very necessary to be clearly understood, 
before one is prepared to enter with profit and delight 
upon the more sublime and interesting field which now 
opens before us. 

We will begin our survey of the heavenly bodies 
with the SUN, which first claims our homage, as the 
natural monarch of the skies. The moon will next oc- 
cupy our attention ; then the other bodies which com- 
pose the solar system, namely, the planets and comets ; 
and, finally, we shall leave behind this little province 
in the great empire of Nature, and wing a bolder flight 
to the fixed stars. 

The distance of the sun from the earth is about 
ninety-five millions of miles. It may perhaps seem in- 
credible to you, that astronomers should be able to de- 
termine this fact with any degree of certainty. Some, 
indeed, not so well informed as yourself, have looked 
upon the marvellous things that are told respecting the 


distances, magnitudes, and velocities, of the heavenly 
bodies, as attempts of astronomers to impose on the 
credulity of the world at large ; but the certainty and 
exactness with which the predictions of astronomers 
are fulfilled, as an eclipse, for example, ought to inspire 
full confidence in their statements. I can assure you, 
my dear friend, that the evidence on which these state- 
ments are founded is perfectly satisfactory to those 
whose attainments in the sciences qualify them to un- 
derstand them ; and, so far are astronomers from wish- 
ing to impose on the unlearned, by announcing such 
wonderful discoveries as they have made among the 
heavenly bodies, no class of men have ever shown a 
stricter regard and zeal than they for the exact truth, 
wherever it is attainable. 

Ninety-five millions of miles is indeed a vast distance. 
No human mind is adequate to comprehend it fully ; 
but the nearest approaches we can make towards it are 
gained by successive efforts of the mind to conceive of 
great distances, beginning with such as are clearly with- 
in our grasp. Let us, then, first take so small a distance 
as that of the breadth of the Atlantic ocean, and follow, in 
mind, a ship, as she leaves the port of New York, and, 
after twenty days' steady sail, reaches Liverpool. Hav- 
ing formed the best idea we are able of this distance, 
we may then reflect, that it would take a ship, moving 
constantly at the rate of ten miles per hour, more than 
a thousand years to reach the sun. 

The diameter of the sun is towards a million of 
miles ; or, more exactly, it is eight hundred and eighty- 
five thousand miles. One hundred and twelve bodies 
as large as the earth, lying side by side, would be re- 
quired to reach across the solar disk ; and our ship, 
sailing at the same rate as before, would be ten years 
in passing over the same space. Immense as is the 
sun, we can readily understand why it appears no 
larger than it does, when we reflect, that its distance is 
still more vast. Even large objects on the earth, when 
seen on a distant eminence, or over a wide expanse of 

THE SUN. 103 

water, dwindle almost to a point. Could we approach 
nearer and nearer to the sun, it would constantly ex- 
pand its volume, until finally it would fill the whole 
vault of heaven. We could, however, approach but 
little nearer to the sun without being consumed by the 
intensity of his heat. Whenever we come nearer to 
any fire, the heat rapidly increases, being four times as 
great at half the distance, and one hundred times as 
great at one tenth the distance. This fact is expressed 
by saying, that the heat increases as the square of the 
distance decreases. Our globe is situated at such a 
distance from the sun, as exactly suits the animal and 
vegetable kingdoms. Were it either much nearer or 
much more remote, they could not exist, constituted as 
they are. The intensity of the solar light also follows 
the same law. Consequently, were we nearer to the sun 
than we are, its blaze would be insufferable ; or, were 
we much further off, the light would be too dim to 
serve all the purposes of vision. 

The sun is one million four hundred thousand times 
as large as the earth ; but its matter is not more than 
about one fourth as dense as that of the earth, being 
only a little heavier than water, while the average den- 
sity of the earth is more than five times that of water. 
Still, on account of the immense magnitude of the sun, 
its entire quantity of matter is three JMpndred and fifty 
thousand times as great as that of the earth. Now, the 
force of gravity in a body is greater, in proportion as 
its quantity of matter is greater. Consequently, we 
might suppose, that the weight of a body (weight being 
nothing else than the measure of the force of gravity) 
would be increased in the same proportion ; or, that a 
body, which weighs only one pound at the surface of 
the earth, would weigh three hundred and fifty thous- 
and pounds at the sun. But we must consider, that the 
attraction exerted by any body is the same as though all 
the matter were concentrated in the centre. Thus, the 
attraction exerted by the earth and by the sun is the 
same as though the entire matter of each body were 


in its centre. Hence, on account of the vast dimen- 
sions of the sun, its surface is one hundred and twelve 
times further from its centre than the surface of the 
earth is from its centre ; and, since the force of gravi- 
ty diminishes as the square of the distance increases, 
that of the sun, exerted on bodies at its surface, is (so 
far as this cause operates) the square of one hundred 
and twelve, or twelve thousand five hundred and for- 
ty-four times less than that of the earth. If, there- 
fore, we increase the weight of a body three hundred 
and fifty-four thousand times, in consequence of the 
greater amount of matter in the sun, and diminish it 
twelve thousand five hundred and forty-four times, in 
consequence of the force acting at a greater distance 
from the body, we shall find that the body would weigh 
about twenty-eight times more on the sun than on the 
earth. Hence, a man weighing three hundred pounds 
would, if conveyed to the surface of the sun, weigh 
eight thousand four hundred pounds, or nearly three 
tons and three quarters. A limb of our bodies, weigh- 
ing forty pounds, would require to lift it a force of one 
thousand one hundred and twenty pounds, which would 
be beyond the ordinary power of the muscles. At the 
surface of the earth, a body falls from rest by the force 
of gravity, in one second, sixteen and one twelfth feet ; 
but at the surface of the sun, a body would, in the same 
time, fall througn four hundred and forty-eight and 
seven tenths feet. 

The sun turns on his own axis once in a little more 
than twenty-five days. This fact is known by observing 
certain dark places seen by the telescope on the sun's 
disk, called solar spots. These are very variable in 
size and number. Sometimes, the sun's disk, when 
viewed with a telescope, is quite free from spots, while 
at other times we may see a dozen or more distinct 
clusters, each containing a great number of spots, some 
large and some very minute. Occasionally, a single 
spot is so large as to be visible to the naked eye, es- 
pecially when the sun is near the horizon, and the glare 

THE SUN. 105 

of his light is taken off. One measured by Dr. Herschel 
was no less than fifty thousand miles in diameter. A 
solar spot usually consists of two parts, the nucleus and 
the umbra. The nucleus is black, of a very irregular 
shape, and is subject to great and sudden changes, both 
in form and size. Spots have sometimes seemed to 
burst asunder, and to project fragments in different di- 
rections. The umbra is a wide margin, of lighter shade, 
and is often of greater extent than the nucleus. The 
spots are usually confined to a zone extending across 
the central regions of the sun, not exceeding sixty de- 
Fig 23 grees in breadth. Fig. 

23 exhibits the appear- 
ance of the solar spots. 
As these spots have all a 
common motion from day 
to day, across the sun's 
disk ; as they go off at 
one limb, and, after a cer- 
tain interval, sometimes 
come on again on the op- 
posite limb, it is inferred 
that this apparent motion 
is imparted to them by 
an actual revolution of the sun on his own axis. We 
know that the spots must be in contact, or very nearly so, 
at least, with the body of the sun, and cannot be bodies 
revolving around it, which are projected on the solar disk 
when they are between us and the sun ; for, in that 
case, they would not be so long in view as out of view, 
as will be evident from inspecting the following dia- 
gram. Let S, Fig. 24, page 106, represent the sun, 
and b a body revolving round it in the orbit a b c ; 
and let E represent the earth, where, of course, the 
spectator is situated. The body would be seen pro- 
jected on the sun only while passing from b to c, while, 
throughout the remainder of its orbit, it would be out 
of view, whereas no such inequality exists in respect to 
the two periods. 



If you ask, what is the cause 
of the solar spots, I can only tell 
you what different astronomers 
have supposed respecting them. 
They attracted the notice of 
Galileo soon after the invention 
of the telescope, and he formed 
an hypothesis respecting their 
nature. Supposing the sun to 
consist of a solid body embosom- 
ed in a sea of liquid fire, he 
believed that the spots are com- 
posed of black cinders, formed 
in the interior of the sun by vol- 
canic action, which rise and float 
on the surface of the fiery sea. 
The chief objections to this hy- 
pothesis are, first, the vast extent 
of some of the spots, covering, 
as they do, two thousand mil- 
lions of square miles, or more, a 
space which it is incredible should be filled by lava in 
so short a time as that in which the spots are sometimes 
formed ; and, secondly, the sudden disappearance which 
the spots sometimes undergo, a fact which can hardly 
be accounted for by supposing, as Galileo did, that such 
a vast accumulation of matter all at once sunk beneath 
the fiery flood. Moreover, we have many reasons for 
believing that the spots are depressions below the gen- 
eral surface. 

La Lande, an eminent French astronomer of the last 
century, held that the sun is a solid, opaque body, hav- 
ing its exterior diversified with high mountains and deep 
valleys, and covered all over with a burning sea of liquid 
matter. The spots he supposed to be produced by the 
flux and reflux of this fiery sea, retreating occasionally 
from the mountains, and exposing to view a portion of 
the dark body of the sun. But it is inconsistent with 
the nature of fluids, that a liquid, like the sea supposed, 

THE SUN. 107 

should depart so far from its equilibrium and remain so 
long fixed, as to lay bare the immense spaces occupied 
by some of the solar spots. 

Dr. Herschel's views respecting the nature and con- 
stitution of the sun, embracing an explanation of the 
solar spots, have, of late years, been very generally re- 
ceived by the astronomical world. This great astrono- 
mer, after attentively viewing the surface of the sun, for 
a long time, with his large telescopes, came to the fol- 
lowing conclusions respecting the nature of this lumi- 
nary. He supposes the sun to be a planetary body like 
our earth, diversified with mountains and valleys, to 
which, on account of the magnitude of the sun, he 
assigns a prodigious extent, some of the mountains 
being six hundred miles high, and the valleys pro- 
portionally deep. He employs in his explanation no 
volcanic fires, but supposes two separate regions of 
dense clouds floating in the solar atmosphere, at differ- 
ent distances from the sun. The exterior stratum of 
clouds he considers as the depository of the sun's light 
and heat, while the inferior stratum serves as an awning 
or screen to the body of the sun itself, which thus be- 
comes fitted to be the residence of animals. The proofs 
offered in support of this hypothesis are chiefly the fol- 
lowing : first, that the appearances, as presented to the 
telescope, are such as accord better with the idea that 
the fluctuations arise from the motions of clouds, than 
that they are owing to the agitations of a liquid, which 
could not depart far enough from its general level to 
enable us to see its waves at so great a distance, where 
a line forty miles in length would subtend an angle at 
the eye of only the tenth part of a second ; secondly, 
that, since clouds are easily dispersed to any extent, the 
great dimensions which the solar spots occasionally ex- 
hibit are more consistent with this than with any other 
hypothesis ; and, finally, that a lower stratum of clouds, 
similar to those of our atmosphere, was frequently seen 
by the Doctor, far below the luminous clouds which are 
the fountains of light and heat. 

Such are the views of one who had, it must be ac- 


knowledged, great powers of observation, and means 
of observation in higher perfection than have ever been 
enjoyed by any other individual ; but, with all defer- 
ence to such authority, I am compelled to think that 
the hypothesis is encumbered with very serious objec- 
tions. Clouds analogous to those of our atmosphere 
(and the Doctor expressly asserts that his lower stratum 
of clouds are analogous to ours, and reasons respecting 
the upper stratum according to the same analogy) can- 
not exist in hot air ; they are tenants only of cold re- 
gions. How can they be supposed to exist in the im- 
mediate vicinity of a fire so intense, that they are even 
dissipated by it at the distance of ninety-five millions 
of miles ? Much less can they be supposed to be the 
depositories of such devouring fire, when any thing 
in the form of clouds, floating in our atmosphere, is 
at once scattered and dissolved by the accession of 
only a few degrees of heat. Nothing, moreover, can 
be imagined more unfavorable for radiating heat to such 
a distance, ttuu^the light, inconstant matter of which 
clouds are composed, floating loosely in the solar at- 
mosphere. There is a logical difficulty in the case : it 
is ascribing to things properties which they are not 
known to possess ; nay, more, which they are known 
not to possess. From variations of light and shade in 
objects seen at moderate distances on the earth, we are 
often deceived in regard to their appearances ; and we 
must distrust the power of an astronomer to decide 
upon the nature of matter seen at the distance of nine- 
ty-five millions of miles. 

I think, therefore, we must confess our ignorance of 
the nature and constitution of the sun ; nor can we, as 
astronomers, obtain much more satisfactory knowledge 
respecting it than the common apprehension, namely, 
that it is an immense globe of fire. We have not yet 
learned what causes are in operation to maintain its un- 
decaying fires ; but our confidence in the Divine wisdom 
and goodness leads us to believe, that those causes 
are such as will preserve those fires from extinction, 
and at a nearly uniform degree of intensity. Any ma- 

THE SUN. 109 

terial change in this respect would jeopardize the safety 
of the animal and vegetable kingdoms, which could not 
exist without the enlivening influence of the solar heat, 
nor, indeed, were that heat any more or less intense 
than it is at present. 

If we, inquire whether the surface of the sun is in a 
state of actual combustion, like burning fuel, or merely 
in a state of intense ignition, like a stone heated to red- 
ness in a furnace, we shall find it most reasonable to 
conclude that it is in a state of ignition. If the body 
of the sun were composed of combustible matter and 
were actually on fire, the material of the sun would be 
continually wasting away, while the products of com- 
bustion would fill all the vast surrounding regions, and 
obscure the solar light. But solid bodies may attain a 
very intense state of ignition, and glow with the most 
fervent heat, while none of their material is consumed, 
and no clouds or fumes rise to obscure their brightness, 
or to impede their further emission of heat. An ignited 
surface, moreover, is far better adapted than flame to the 
radiation of heat. Flame, when made* to act in contact 
with the surfaces of solid bodies, heats them rapidly 
and powerfully ; but it sends forth, or radiates, very 
little heat, compared with solid matter in a high state 
of ignition. These various considerations render it 
highly probable to my mind, that the body of the sun 
is not in a state of actual combustion, but merely in a 
state of high ignition. 

The solar beam consists of a mixture of several dif- 
ferent sorts of rays. First, there are the calorific rays, 
which afford heat, and are entirely distinct from those 
which afford light, and may be separated from them. 
Secondly, there are the colorific rays, which give light, 
consisting of rays of seven distinct colors, namely, vio- 
let, indigo, blue, green, yellow, orange, red. These, 
when separated, as they may be by a glass prism, com- 
pose the prismatic spectrum. They appear also in the 
rainbow. When united again, in due proportions, they 
constitute white light, as seen in the light of the sun. 

10 L. A. 


Thirdly, there are found in the solar beam a class of 
rays which afford neither heat nor light, but which 
produce chemical changes in certain bodies exposed to 
their influence, and hence are called chemical rays. 
Fourthly, there is still another class, called magnetiz- 
ing rays, because they are capable of imparting mag- 
netic properties to steel. These different sorts of rays 
are sent forth from the sun, to the remotest regions of 
the planetary worlds, invigorating all things by their 
life-giving influence, and dispelling the darkness that 
naturally fills all space. 

But it was not alone to give heat and light, that the 
sun was placed in the firmament. By his power of at- 
traction, also, he serves as the great regulator of the 
planetary motions, bending them continually from the 
straight line in which they tend to move, and compel- 
ling them to circulate around him, each at nearly a 
uniform distance, and all in perfect harmony. I will 
hereafter explain to you the manner in which the grav- 
ity of the sun thus acts, to control the planetary mo- 
tions. For the present, let us content ourselves with 
reflecting upon the wonderful force which the sun must 
put forth, in order to bend out of their courses, into cir- 
cular orbits, such a number of planets, some of which 
are more than a thousand times as large as the earth. 
Were a ship of war under full sail, and it should be re- 
quired to turn her aside from her course by a rope at- 
tached to her bow, we can easily imagine that it would 
take a great force to do it, especially were it required 
that the force should remain stationary and the ship 
be so constantly diverted from her course, as to be 
made to go round the force as round a centre. Some- 
what similar to this is the action which the sun exerts 
on each of the planets by some invisible influence, called 
gravitation. The bodies which he thus turns out of 
their course, and bends into a circular orbit around him- 
self, are, however, many millions of times as ponderous 
as the ship, and are moving many thousand times as 




*' These, as they change, Almighty Father, these 
Are but the varied God. The rolling year 
Is full of Thee." Thomson. 

WE have seen that the apparent revolution of the 
heavenly bodies, from east to west, every twenty-four 
hours, is owing to a real revolution of the earth on its 
own axis, in the opposite direction. This motion is 
very easily understood, resembling, as it does, the spin- 
ning of a top. We must, however, conceive of the top 
as turning without any visible support, and not as rest- 
ing in the usual manner on a plane. The annual mo- 
tion of the earth around the sun, which gives rise to an 
apparent motion of the sun around the earth once a 
year, and occasions the change of seasons, is somewhat 
more difficult to understand ; and it may cost you some 
reflection, before you will settle all the points respect- 
ing the changes of the seasons clearly in your mind. 
We sometimes see these two motions exemplified in a 
top. When, as the string is pulled, the top is thrown 
forwards on the floor, we may see it move forward 
(sometimes in a circle) at the same time that it spins 
on its axis. Let a candle be placed on a table, to rep- 
resent the sun, and let these two motions be imagined 
to be given to a top around it, and we shall have a case 
somewhat resembling the actual motions of the earth 
around the sun. 

When bodies are at such a distance from each other 
as the earth and the sun, a spectator on either would 
project the other body upon the concave sphere of the 
heavens, always seeing it on the opposite side of a 
great circle one hundred and eighty degrees from 

Recollect that the path in which the earth move*' 



round the sun is called the ecliptic. We are not to 
conceive of this, or of any other celestial circle, as hav- 
ing any real, palpable existence, any more than the path 
of a bird through the sky. You will perhaps think it 
quite superfluous for me to remind you of this ; but, 
from the habit of seeing the orbits of the heavenly bod- 
ies represented in diagrams and orreries, by palpable 
lines and circles, we are apt inadvertently to acquire 
the notion, that the orbits of the planets, and other rep- 
resentations of the artificial sphere, have a real, pal- 
pable existence in Nature ; whereas, they denote the 
places where mere geometrical or imaginary lines run. 
You might have expected to see an orrery, exhibiting 
a view of the sun and planets, with their various mo- 
tions, particularly described in my Letter on astronom- 
ical instruments and apparatus. I must acknowledge, 
that I entertain a very low opinion of the utility of even 
the best orreries, and I cannot recommend them as 
auxiliaries in the study of astronomy. The numerous 
appendages usually connected with them, some to sup- 
port them in a proper position, and some to communi- 
cate to them the requisite motions, enter into the ideas 
which the learner forms respecting the machinery of 
the heavens ; and it costs much labor afterwards to di- 
vest the mind of such erroneous impressions. Astron- 
omy can be exhibited much more clearly and beauti- 
fully to the mental eye than to the visual organ. It is 
much easier to conceive of the sun existing in bound- 
less space, and of the earth as moving around him at a 
great distance, the mind having nothing in view but 
simply these two bodies, than it is, in an orrery, to con- 
template the motion of a ball representing the earth, 
carried by a complicated apparatus of wheels around 
another ball, supported by a cylinder or wire, to repre- 
sent the sun. I would advise you, whenever it is prac- 
ticable, to think how things are in Nature, rather than 
how they are represented by art. The machinery of 
the heavens is much simpler than that of an orrery. 
In endeavoring to obtain a clear idea of the revolu- 


tion of the earth around the sun, imagine to yourself a 
plane (a geometrical plane, having merely length and 
breadth, but no thickness) passing through the centres of 
the sun and the earth, and extended far beyond the earth 
till it reaches the firmament of stars. Although, in- 
deed, no such dome actually exists as that under which 
we figure to ourselves the vault of the sky, yet, as the 
fixed stars appear to be set in such a dome, we may 
imagine that the circles of the sphere, when indefinite- 
ly enlarged, finally reach such an imaginary vault. All 
that is essential is, that we should imagine this to ex- 
ist far beyond the bounds of the solar system, the vari- 
ous bodies that compose the latter being situated close 
around the sun, at the centre. 

Along the line where this great circle meets the star- 
ry vault, are situated a series of constellations, Aries, 
Taurus, Gemini, &c., which occupy successively this 
portion of the heavens. When bodies are at such a 
distance from each other as the sun and the earth, I 
have said that a spectator on either would project the 
other body upon the concave sphere of the heavens, 
always seeing it on the opposite side of a great circle 
one hundred and eighty degrees from himself. The 
place of a body, when viewed from any point, is denot- 
ed by the position it occupies among the stars. Thus, 
in the diagram, Fig. 25, page 114, when the earth ar- 
rives at E, it is said to be in Aries, because, if viewed 
from the sun, it would be projected on that part of the 
heavens ; and, for the same reason, to a spectator at 
E, the sun would be in Libra. When the earth shifts 
its position from Aries to Taurus, as we are unconscious 
of our own motion, the sun it is that appears to move 
from Libra to Scorpio, in the opposite part of the heav- 
ens. Hence, as we go forward, in the order of the 
signs, on one side of the ecliptic, the sun seems to be 
moving forward at the same rate on the opposite side 
of the same great circle ; and therefore, although we 
are unconscious of our own motion, we can read it, from 
day to day, in the motions of the sun. If we could see 


Fig. 25. 

the stars at the same time with the sun, we could actu- 
ally observe, from day to day, the sun's progress through 
them, as we observe the progress of the moon at night ; 
only the sun's rate of motion would be nearly fourteen 
times slower than that of the moon. Although we do 
not see the stars when the sun is present, we can observe 
that it makes daily progress eastward, as is apparent 
from the constellations of the zodiac occupying, succes- 
sively, the western sky immediately after sunset, prov- 
ing that either all the stars have a common motion 
westward, independent of their diurnal motion, or that 
the sun has a motion past them from west to east. We 
shall see, hereafter, abundant evidence to prove, that 
this change in the relative position of the sun and stars, 
is owing to a change in the apparent place of the sun, 
and not to any change in the stars. 

To form a clear idea of the two motions of the earth, 
imagine yourself standing on a circular platform which 


turns slowly round its centre. While you are carried 
slowly round the entire of the circuit of the heavens, 
along with the platform, you may turn round upon your 
heel the same way three hundred and sixty-five times. 
The former is analogous to our annual motion with the 
earth around the sun ; the latter, to our diurnal revolu- 
tion in common with the earth around its own axis. 

Although the apparent revolution of the sun is in a 
direction opposite to the real motion of the earth, as re- 
gards absolute space, yet both are nevertheless from 
west to east, since these terms do not refer to any di- 
rections in absolute space, but to the order in which 
certain constellations (the constellations of the Zodiac) 
succeed one another. The earth itself, on opposite 
sides of its orbit, does in fact move towards directly op- 
posite points of space ; but it is all the while pursuing 
its course in the order of the signs. In the same man- 
ner, although the earth turns on its axis from west to 
east, yet any place on the surface of the earth is moving 
in a direction in space exactly opposite to its direction 
twelve hours before. If the sun left a visible trace on 
the face of the sky, the ecliptic would of course be dis- 
tinctly marked on the celestial sphere, as it is on an 
artificial globe ; and were the equator delineated in a 
similar manner, we should then see, at a glance, the 
relative position of these two circles, the points where 
they intersect one another, constituting the equinoxes ; 
the points where they are at the greatest distance asun- 
der, that is, the solstices ; and various other particu- 
lars, which, for want of such visible traces, we are now 
obliged to search for by indirect and circuitous methods. 
It will aid you, to have constantly before your mental 
vision an imaginary delineation of these two important 
circles on the face of the sky. 

The equator makes an angle with the ecliptic of 
twenty-three degrees and twenty-eight minutes. This 
is called the obliquity of the ecliptic. As the sun and 
earth are both always in the ecliptic, and as the motion 
of the earth in one part of it makes the sun appear to 


move in the opposite part, at the same rate, the sun ap- 
parently descends, in Winter, twenty-three degrees and 
twenty-eight minutes to the south of the equator, and 
ascends, in Summer, the same number of degrees north 
of it. We must keep in mind, that the celestial equa- 
tor and celestial ecliptic are here understood, and we 
may imagine them to be two great circles delineated on 
the face of the sky. On comparing observations made 
at different periods, for more than two thousand years, 
it is found, that the obliquity of the ecliptic is not 
constant, but that it undergoes a slight diminution, from 
age to age, amounting to fifty-two seconds in a century, 
or about half a second annually. We might apprehend 
that, by successive approaches to each other, the equa- 
tor and ecliptic would finally coincide ; but astronomers 
have discovered, by a most profound investigation, based 
on the principles of universal gravitation, that this irreg- 
ularity is confined within certain narrow limits ; and that 
the obliquity, after diminishing for some thousands of 
years, will then increase for a similar period, and will 
thus vibrate forever about a mean value. 

As the earth traverses every part of her orbit in the 
course of a year, she will be once at each solstice, and 
once at each equinox. The best way of obtaining a 
correct idea of her two motions is, to conceive of her 
as standing still for a single day, at some point in her 
orbit, until she has turned once on her axis, then mov- 
ing about a degree, and halting again, until another 
diurnal revolution is completed. Let us suppose the 
earth at the Autumnal equinox, the sun, of course, be- 
ing at the Vernal equinox, for we must always think of 
these two bodies as diametrically opposite to each other. 
Suppose the earth to stand still in its orbit for twenty- 
four hours. The revolution of the earth on its axis, 
from west to east, will make the sun appear to describe 
a great circle of the heavens from east to west, coincid- 
ing with the equator. At the end of this period, sup- 
pose the sun to move northward one degree, and to 
remain there for twenty-four hours ; in which time, the 


revolution of the earth, will make the sun appear to 
describe another circle, from east to west, parallel to the 
equator, but one degree north of it. Thus, we may 
conceive of the sun as moving one degree north, every 
day, for about three months, when it will reach the point 
of the ecliptic furthest from the equator, which point is 
called the tropic, from a Greek word, signifying to turn ; 
because, after the sun has passed this point, his motion 
in his orbit carries him continually towards the equator, 
and therefore he seems to turn about. The same point 
is also called the solstice, from a Latin word, signify- 
ing to stand still ; since, when the sun has reached its 
greatest northern or southern limit, while its declina- 
tion is at the point where it ceases to increase, but be- 
gins to decrease, there the sun seems for a short time 
stationary, with regard to the equator, appearing for 
several days to describe the same parallel of latitude. 

When the sun is at the northern tropic, which hap- 
pens about the twenty-first of June, his elevation above 
the southern horizon at noon is the greatest in the 
year ; and when he is at the southern tropic, about the 
twenty-first of December, his elevation at noon is the 
least in the year. The difference between these two 
meridian altitudes will give the whole distance from 
one tropic to the other, and consequently, twice the dis- 
tance from each tropic to the equator. By this means, 
we find how far the tropic is from the equator, and that 
gives us the angle which the equator and ecliptic make 
with each other ; for the greatest distance between any 
two great circles on the sphere is always equal to the 
angle which they make with each other. Thus, the 
ancient astronomers were able to determine the obliqui- 
ty of the ecliptic with a great degree of accuracy. It 
was easy to find the situation of the zenith, because the 
direction of a plumb-line shows us where that is ; and 
it was easy to find the distances from the zenith where 
the sun was at the greatest and least distances, respec- 
tively. The difference of these two arcs is the angu- 
lar distance from one tropic to the other ; and half this 


arc is the distance of either tropic from the equator, 
and of course, equal to the obliquity of the ecliptic. 
All this will be very easily understood from the annexed 
diagram, Fig. 26. Let Z be 
the zenith of a spectator sit- 
uated at C ; Z n the least, 
and Z s the greatest distance 
of the sun from the zenith. 
From Z s subtract Z n, and 
then s n, the difference, di- 
vided by two, will give the 
obliquity of the ecliptic. 

The motion of the earth 
in its orbit is nearly seventy 
times as great as its greatest 
motion around its axis. In its revolution around the 
sun, the earth moves no less than one million six hun- 
dred and forty thousand miles per day, sixty-eight thous- 
and miles per hour, eleven hundred miles per minute, 
and nearly nineteen miles every second ; a velocity near- 
ly sixty times as great as the greatest velocity of a can- 
non ball. Places on the earth turn with very different 
degrees of velocity in different latitudes. Those near 
the equator are carried round on the circumference of 
a large circle ; those towards the poles, on the circum- 
ference of a small circle ; while one standing on the 
pole itself would not turn at all. Those who live on 
the equator are carried about one thousand miles an 
hour. In our latitude, (forty-one degrees and eighteen 
minutes,) the diurnal velocity is about seven hundred 
and fifty miles per hour. It would seem, at first view, 
quite incredible, that we should be whirled round at so 
rapid a rate, and yet be entirely insensible of any mo- 
tion ; and much more, that we could be going so swiftly 
through space, in our circuit around the sun, while all 
things, when unaffected by local causes, appear to be 
in such a state of quiescence. Yet we have the most 
unquestionable evidence of the fact ; nor is it difficult 
to account for it, in consistency with the general state 


of repose among bodies on the earth, when we reflect 
that their relative motions, with respect to each other, 
are not in the least disturbed by any motions which 
they may have in common. When we are on board a 
steam-boat, we move about in the same manner when 
the boat is in rapid motion, as when it is lying still ; 
and such would be the case, if it moved steadily a hun- 
dred times faster than it does. -Were the earth, how- 
ever, suddenly to stop its diurnal revolution, all movable 
bodies on its surface would be thrown off in tangents 
to the surface with velocities proportional to that of their 
diurnal motion ; and were the earth suddenly to halt in 
its orbit, we should be hurled forward into space with 
inconceivable rapidity. 

I will next endeavor to explain to you the phenom- 
ena of the Seasons. These depend on two causes; 
first, the inclination of the earth's axis to the plane of 
its orbit ; and, secondly, to the circumstance, that the 
axis always remains parallel to itself. Imagine to your- 
self a candle placed in the centre of a ring, to represent 
the sun in the centre of the earth's orbit, and an apple 
with a knittingneedle running through it in the direc- 
tion of the stem. Run a knife around the central part 
of the apple, to mark the situation of the equator. The 
circumference of the ring represents the earth's orbit 
in the plane of the ecliptic. Place the apple so that 
the equator shall coincide with the wire ; then the axis 
will lie directly across the plane of the ecliptic ; that is, 
at right angles to it. Let the apple be carried quite 
round the ring, constantly preserving the axis parallel 
to itself, and the equator all the while coinciding with 
the wire that represents the orbit. Now, since the sun 
enlightens half the globe at once, so the candle, which 
here represents the sun, will shine on the half of the 
apple that is turned towards it ; and the circle which 
divides the enlightened from the unenlightened side of 
the apple, called the terminator, will pass through both 
the poles. If the apple be turned slowly round on its 
axis, the terminator will successively pass over all places 


on the earth, giving the appearance of sunrise to places 
at which it arrives, and of sunset to places from which 
it departs. If, therefore, the equator had coincided with 
the ecliptic, as would have been the case, had the earth's 
axis been perpendicular to the plane of its orbit, the 
diurnal motion of the sun would always have been in 
the equator, and the days and nights would have been 
equal all over the globe. To the inhabitants of the 
equatorial parts of the earth, the sun would always have 
appeared to move in the prime vertical, rising directly 
in the east, passing through the zenith at noon, and 
setting in the west. In the polar regions, the sun would 
always have appeared to revolve in the horizon ; while, 
at any place between the equator and the pole, the 
course of the sun would have been oblique to the hori- 
zon, but always oblique in the same degree. There 
would have been nothing of those agreeable vicissitudes 
of the seasons which we now enjoy ; but some regions 
of the earth would have been crowned with perpetual 
spring, others would have been scorched with the unre- 
mitting, fervor of a vertical sun, while extensive regions 
towards either pole would have been consigned to ever- 
lasting frost and sterility. 

To understand, then, clearly, the causes of the change 
of seasons, use the same apparatus as before ; but, in- 
stead of placing the axis of the earth at right angles to 
the plane of its orbit, turn it out of a perpendicular po- 
sition a little, (twenty-three degrees and twenty-eight 
minutes,) then the equator will be turned just the same 
number of degrees out of a coincidence with the ecliptic. 
Let the apple be carried around the ring, always hold- 
ing the axis inclined at the same angle to the plane of 
the ring, and always parallel to itself. You will find 
that there will be two points in the circuit where the 
plane of the equator, that you had marked around the 
centre of the apple, will pass through the centre of the 
sun ; these will be the points where the celestial equa- 
tor and the ecliptic cut one another, or the equinoxes. 
When the earth is at either of these points, the sun 


shines on both poles alike ; and, if we conceive of the 
earth, while in this situation, as turning once round on 
its axis, the apparent diurnal motion of the sun will be 
the same as it would be, were the earth's axis perpen- 
dicular to the plane of the equator. For that day, the 
sun would revolve in the equator, and the days and 
nights would be equal all over the globe. If the apple 
were carried round in the manner supposed, then, at 
the distance of ninety degrees from the equinoxes, the 
same pole would be turned from the sun on one side, 
just as much as it was turned towards him on the other. 
In the former case, the sun's light would fall short of the 
pole twenty-three and one half degrees, and in the other 
case, it would reach beyond it the same number of de- 
grees. I would recommend to you to obtain as clear 
an idea as you can of the cause of the change of sea- 
sons, by thinking over the foregoing illustration. You 
may then clear up any remaining difficulties, by study- 
ing the diagram, Fig. 27, on page 122. 

Let A B C D represent the earth's place in different 
parts of its orbit, having the sun in the centre. Let 

A, C, be the positions of the earth at the equinoxes, and 

B, D, its positions at the tropics, the axis n s being al- 
ways parallel to itself. It is difficult to represent things 
of this kind correctly, all on the same plane ; but you 
will readily see, that the figure of the earth, here, an- 
swers to the apple in the former illustration ; that the 
hemisphere towards n is above, and that towards s is 
below, the plane of the paper. When the earth is at 
A and C, the Vernal and Autumnal equinoxes, the sun, 
you will perceive, shines on both the poles n and s ; and, 
if you conceive of the globe, while in this position, as 
turned round on its axis, as it is in the diurnal revolu- 
tion, you will readily understand, that the sun would 
describe the celestial equator. This may not at first 
appear so obvious, by inspecting the figure ; but if you 
consider the point n as raised above the plane of the 
paper, and the point s as depressed below it, you will 
readily see how the plane of the equator would pass 

11 L. A. 


Fig. 27. 


through the centre of the sun. Again, at B, when the 
earth is at the southern tropic, the sun shines twenty- 
three and a half degrees beyond the north pole, n, and 
falls the same distance short of the south pole, s. The 
case is exactly reversed when the earth is at the north- 
ern tropic, and the sun at the southern. While the 
earth is at one of the tropics, at B, for example, let us 
conceive of it as turning on its axis, and we shall read- 
ily see, that all that part of the earth which lies within 
the north polar circle will enjoy continual day, while 
that within the south polar circle will have continual 
night ; and that all other places will have their days 
longer as they are nearer to the enlightened pole, and 
shorter as they are nearer to the unenlightened pole. 


This figure likewise shows the successive positions of 
the earth, at different periods of the year, with respect 
to the signs, and what months correspond to particular 
signs. Thus, the earth enters Libra, and the sun Aries, 
on the twenty-first of March, and on the twenty-first 
of June, the earth is just entering Capricorn, and the 
sun, Cancer. You will call to mind what is meant 
by this phraseology, that by saying the earth enters 
Libra, we mean that a spectator placed on the sun 
would see the earth in that part of the celestial ecliptic, 
which is occupied by the sign Libra ; and that a spec- 
tator on the earth sees the sun at the same time pro- 
jected on the opposite part of the heavens, occupied by 
the sign Cancer. 

Had the axis of the earth been perpendicular to the 
plane of the ecliptic, then the sun would always have 
appeared to move in the equator, the days would every 
where have been equal to the nights x and there could 
have been no change of seasons. On the other hand, 
had the inclination of the ecliptic to the equator been 
much greater than it is, the vicissitudes of the seasons 
would have been proportionally greater, than at present. 
Suppose, for instance, the equator had been at right 
angles to the ecliptic, in which case, the poles of the 
earth would have been situated in the ecliptic itself; 
then, in different parts of the earth, the appearances 
would have been as follows : To a spectator on the 
equator, (where all the circles of diurnal revolution are 
perpendicular to the horizon,) the sun, as he left the 
vernal equinox, would every day perform his diurnal 
revolution in a smaller and smaller circle, until he reach- 
ed the north pole, when he would halt for a moment, 
and then wheel about and return to the equator, in a 
reverse order. The progress of the sun through the 
southern signs, to the south pole, would be similar to 
that already described. Such would be the appear- 
ances to an inhabitant of the equatorial regions. To a 
spectator living in an oblique sphere, in our own lati- 
tude, for example, the sun, while north of the equator, 


would advance continually northward, making his diur- 
nal circuit in parallels further and further distant from 
the equator, until he reached the circle of perpetual 
apparition ; after which, he would climb, by a spiral 
course, to the north star, and then as rapidly return to 
the equator. By a similar progress southward, the sun 
would at length pass the circle of perpetual occultation, 
and for some time (which would be longer or shorter, 
according to the latitude of the place of observation) 
there would be continual night. To a spectator on the 
pole of the earth and under the pole of the heaven, 
during the long day of six months, the sun would wind 
its way to a point directly over head, pouring down 
upon the earth beneath not merely the heat of the tor- 
rid zone, but the heat of a torrid noon, accumulating 
without intermission. 

The great vicissitudes of heat and cold, which would 
attend these several movements of the sun, would be 
wholly incompatible with the existence of either the 
animal or the vegetable kingdom, and all terrestria 1 Na- 
ture would be doomed to perpetual sterility and deso- 
lation. The happy provision which the Creator has 
made against such extreme vicissitudes, by confining 
the changes of the seasons within such narrow bounds, 
conspires with many other express arrangements in the 
economy of Nature, to secure the safety and comfort 
of the human race. 

Perhaps you have never reflected upon all the rea- 
sons, why the several changes of position, with respect 
to the horizon, which the sun undergoes in the course 
of the year, occasion such a difference in the amount 
of heat received from him. Two causes contribute to 
increase the heat of Summer and the cold of Winter. 
The higher the sun ascends above the horizon, the more 
directly his rays fall upon the earth ; and their heating 
power is rapidly augmented, as they approach a per- 
pendicular direction. When the sun is nearly over 
head, his rays strike us with far greater force than when 
they meet us obliquely ; and the earth absorbs a far 


greater number of those rays of heat which strike it 
perpendicularly, than of those which meet it in a slant- 
ing direction. When the sun is near the horizon, his 
rays merely glance along the ground, and many of them, 
before they reach it, are absorbed and dispersed in pass- 
ing through the atmosphere. Those who have felt only 
the oblique solar rays, as they fall upon objects in the 
high latitudes, have a very inadequate idea of the pow- 
er of a vertical, noonday sun, as felt in the region of 
the equator. 

The increased length of the day in Summer is anoth- 
er cause of the heat of this season of the year. This 
cause more sensibly affects places far removed from the 
equator, because at such places the days are longer 
and the nights shorter than in the torrid zone. By the 
operation of this cause, the solar heat accumulates there 
so much, during the longest days of Summer, that the 
temperature rises to a higher degree than is often known 
in the torrid climates. 

EJrt the temperature of a place is influenced very 
much by several other causes, as well as by the force 
and duration of the sun's heat. First, the elevation of 
a country above the level of the sea has a great influ- 
ence upon its climate. Elevated districts of country, 
even in the torrid zone, often enjoy the most agreeable 
climate in the world. The cold of the upper regions 
of the atmosphere modifies and tempers the solar heat, 
so as to give a most delightful softness, while the uni- 
formity of temperature excludes those sudden and ex- 
cessive changes which are often experienced in less 
favored climes. In ascending certain high mountains 
situated within the torrid zone, the traveller passes, in 
a short time, through every variety of climate, from the 
most oppressive and sultry heat, to the soft and balmy 
air of Spring, which again is succeeded by the cooler 
breezes of Autumn, and then by the severest frosts of 
Winter. A corresponding difference is seen in the 
products of the vegetable kingdom. While Winter 
reigns on the summit of the mountain, its central re- 


gions may be encircled with the verdure of Spring, and 
its base with the flowers and fruits of Summer. Sec- 
ondly, the proximity of the ocean also has a great effect 
to equalize the temperature of a place. As the ocean 
changes its temperature during the year much less than 
the land, it becomes a source of warmth to contiguous 
countries in Winter, and a fountain of cool breezes in 
Summer. Thirdly, the relative humidity or dryness 
of the atmosphere of a place is of great importance, in 
regard to its effects on the animal system. A dry air 
of ninety degrees is not so insupportable as a humid air 
of eighty degrees ; and it may be asserted as a general 
principle, that a hot and humid atmosphere is unhealthy, 
although a hot air, when dry, may be very salubrious. 
In a warm atmosphere which is dry, the evaporation 
of moisture from the surface of the body is rapid, and 
its cooling influence affords a most striking relief to an 
intense heat without ; but when the surrounding atmos- 
phere is already filled with moisture, no such evapora- 
tion takes place from the surface of the skin, and no 
such refreshing effects are experienced from this cause. 
Moisture collects on the skin ; a sultry, oppressive sen- 
sation is felt ; and chills and fevers are usually in the 



; What though in solemn silence, all 

Move round this dark, terrestrial ball ! 

In reason's ear they all rejoice, 

And utter forth a glorious voice ; 

For ever singing, as they shine, 
' The hand that made us is divine.' " Addison. 

HOWEVER incredible it may seem, no fact is more 
certain, than that the earth is constantly on the wing, 
flying around the sun with a velocity so prodigious, that, 
for every breath we draw, we advance on our way forty 


or fifty miles. If, when passing across the waters in 
a steam-boat, we can wake, after a night's repose, 
and find ourselves conducted on our voyage a hundred 
miles, we exult in the triumphs of art, which could have 
moved so ponderous a body as a steam-ship over such 
a space in so short a time, and so quietly, too, as not to 
disturb our slumbers ; but, with a motion vastly more 
quiet and uniform, we have, in the same interval, been 
carried along with the earth in its orbit more than half 
a million of miles. In the case of the steam-ship, how- 
ever perfect the machinery may be, we still, in our 
waking hours at least, are made sensible of the action 
of the forces by which the motion is maintained, as 
the roaring of the fire, the beating of the piston, and 
the dashing of the paddle-wheels ; but in the more 
perfect machinery which carries the earth forward on 
her grander voyage, no sound is heard, nor the least in- 
timation afforded of the stupendous forces by which this 
motion is achieved. To the pious observer of Nature 
it might seem sufficient, without any inquiry into sec- 
ond causes, to ascribe the motions of the spheres to the 
direct agency of the Supreme Being. If, however, we 
can succeed in finding the secret springs and cords, by 
which the motions of the heavenly bodies are immedi- 
ately produced and controlled, it will detract nothing 
from our just admiration of the Great First Cause of all 
things. We may therefore now enter upon the inquiry 
into the nature or laws of the forces by which the earth 
is made to revolve on her axis and in her orbit ; and 
having learned what it is, that causes and maintains the 
motions of the earth, you will then acquire, at the same 
time, a knowledge of all the celestial machinery. The 
subject will involve an explanation of the laws of mo- 
tion, and of th principles of universal gravitation. 

It was once? supposed, that we could never reason re- 
specting the laws that govern the heavenly bodies from 
what we observe in bodies around us, but that motion 
is one thing on the earth and quite another thing in the 
skies ; and hence, that it is impossible for us, by any 


inquiries into the laws of terrestrial Nature, to ascertain 
how things take place among the heavenly bodies. 
Galileo and Newton, however, proceeded on the con- 
trary supposition, that Nature is uniform in all her 
works ; that the same Almighty arm rules over all ; and 
that He works by the same fixed laws through all parts 
of His boundless realm. The certainty with which all 
the predictions of astronomers, made on these supposi- 
tions, are fulfilled, attest the soundness of the hypoth- 
esis. Accordingly, those laws, which all experience, 
endlessly multiplied and varied, proves to be the laws 
of terrestrial motion, are held to be the laws that gov- 
ern also the motions of the most distant planets and 
stars, and to prevail throughout the universe of matter. 
Let us, then, briefly review these great laws of motion, 
which are three in number. The FIRST LAW is as fol- 
lows : every body perseveres in a state of rest, or of 
uniform motion in a straight line, unless compelled 
by some force to change its state. By force is meant 
any thing which produces motion. 

The foregoing law has been fully established by ex- 
periment, and is conformable to all experience. It em- 
braces several particulars. First, a body, when at rest, 
remains so, unless some force puts it in motion ; and 
hence it is inferred, when a body is found in motion, 
that some force must have been applied to it sufficient 
to have caused its motion. Thus, the fact, that the 
earth is in motion around the sun and around its own 
axis, is to be accounted for by assigning to each of 
these motions a force adequate, both in quantity and 
direction, to produce these motions, respectively. 

Secondly, when a body is once in motion, it will 
continue to move for ever, unless something stops it. 
When a ball is struck on the surface of the earth, the 
friction of the earth and the resistance of the air soon 
stop its motion ; when struck on smooth ice, it will 
go much further before it comes to a state of rest, be- 
cause the ice opposes much less resistance than the 
ground ; and, were there no impediment to its motion. 


it would, when once set in motion, continue to move 
without end. The heavenly bodies are actually in this 
condition : they continue to move, not because any new 
forces are applied to them ; but, having been once set 
in motion, they continue in motion because there is 
nothing to stop them. This property in bodies to per- 
severe in the state they are actually in, if at rest, to 
remain at rest, or, if in motion, to continue in mo- 
tion, is called inertia. The inertia of a body (which 
is measured by the force required to overcome it) is 
proportioned to the quantity of matter it contains. A 
steam-boat manifests its inertia, on first starting it, by 
the enormous expenditure of force required to bring it 
to a given rate of motion ; and it again manifests its 
inertia, when in rapid motion, by the great difficulty of 
stopping it. The heavenly bodies, having been once 
put in motion, and meeting with nothing to stop them, 
move on by their own inertia. A top affords a beauti- 
ful illustration of inertia, continuing, as it does, to spin 
after the moving force is withdrawn. 

Thirdly, the motion to which a body naturally tends 
is uniform ; that is, the body moves just as far the sec- 
ond minute as it did the first, and as far the third as the 
second ; and passes over equal spaces in equal times. 
I do not assert that the motion of all moving bodies is 
in fact uniform, but that such is their tendency. If it 
is otherwise than uniform, there is some cause operating 
to disturb the uniformity to which it is naturally prone. 

Fourthly, a body in motion will move in a straight 
lim, unless diverted out of that line by some external 
force ; and the body will resume its straight-forward 
motion, whenever the force that turns it aside is with- 
drawn. Every body that is revolving in an orbit, like 
the moon around the earth, or the earth around the 
sun, tends to move in a straight line which is a tangent* 
to its orbit. Thus, if A B C, Fig. 28, represents the 
orbit of the moon around the earth, were it not for the 

* A tangent is a straight line touching a circle, as A D, in Fig. 28. 


constant action of some force that draws her towards 
the earth, she would move off in a straight line. If the 
force that carries her towards the earth were suspended 
at A, she would immediately desert the circular motion, 
and proceed in the direction AD. In the same man- 
ner, a boy whirls a stone around his head in a sling, 
and then letting go one of the strings, and releasing the 
force that binds it to the circle, it flies off in a straight 
line which is a tangent to that part of the circle where 
it was released. This tendency which a body revolving 
in an orbit exhibits, to recede from the centre and to fly 
ofT in a tangent, is called the centrifugal force. We 
see it manifested when a pail of water is whirled. The 
water rises on the sides of the vessel, leaving a hollow 
in the central parts. We see an example of the effects 
of centrifugal action, when a horse turns swiftly round 
a corner, and the rider is thrown outwards ; also, when 
a wheel passes rapidly through a small collection of 
water, and portions of the water are thrown off from 
the top of the wheel in straight lines which are tangents 
to the wheel. 

The centrifugal force is increased as the velocity is 
increased. Thus, the parts of a millstone most remote 
from the centre sometimes acquire a centrifugal force 


so much greater than the central parts, which move 
much slower, that the stone is divided, and the exterior 
portions are projected with great violence. In like 
manner, as the equatorial parts of the earth, in the 
diurnal revolution, revolve much faster than the parts 
towards the poles, so the centrifugal force is felt most 
at the equator, and becomes strikingly manifest by the 
diminished weight of bodies, since it acts in opposition 
to the force of gravity. 

Although the foregoing law of motion, when first 
presented to the mind, appears to convey no new truth, 
but only to enunciate in a formal manner what we 
knew before ; yet a just understanding of this law, in all 
its bearings, leads us to a clear comprehension of no 
small share of all the phenomena of motion. The 
second and third laws may be explained in fewer terms. 

The SECOND LAW of motion is as follows : motion is 
proportioned to the force impressed, and in the direc- 
tion of that force. 

The meaning of this law is, that every force that is 
applied to a body produces its full effect, proportioned 
to its intensity, either in causing or in preventing mo- 
tion. Let there be ever so many blows applied at once 
to a ball, each will produce its own effect in its own 
direction, and the ball will move off, not indeed in the 
zigzag, complex lines corresponding to the directions 
of the several forces, but in a single line expressing 
the united effect of all. If you place a ball at the cor- 
ner of a table, and give it an impulse, at the same in- 
stant, with the thumb and finger of each hand, one im- 
pelling it in the direction of one side of the table, and 
the other in the direction of the other side, the ball will 
move diagonally across the table. If the blows be ex- 
actly proportioned each to the length of the side of the 
table on which it is directed, the ball will run exactly 
from corner to corner, and in the same time that it 
would have passed over each side by the blow given in 
the direction of that side. This principle is expressed 
by saying, that a body impelled by two forces, acting 


respectively in the directions of the two sides of a par- 
allelogram, and proportioned in intensity to the lengths 
of the sides, will describe the diagonal of the parallelo- 
gram in the same time in which it would have described 
the sides by the forces acting separately. 

The converse of this proposition is also true, namely, 
that any single motion may be considered as the result- 
ant of two others, the motion itself being represented 
by the diagonal, while the two components are repre- 
sented by the sides, of a parallelogram. This reduction 
of a motion to the individual motions that produce it, 
is called the resolution of motion, or the resolution of 
forces. Nor can a given motion be resolved into two 
components, merely. These, again, may be resolved 
into others, varying indefinitely, in direction and inten- 
sity, from all which the given motion may be considered 
as having resulted. This composition and resolution 
of motion or forces is often of great use, in inquiries 
into the motions of the heavenly bodies. The compo- 
sition often enables us to substitute a single force for 
a great number of others, whose individual operations 
would be too complicated to be followed. By this 
means, the investigation is greatly simplified. On the 
other hand, it is frequently very convenient to resolve 
a given motion into two or more others, some of which 
may be thrown out of the account, as not influencing 
the particular point which we are inquiring about, while 
others are far more easily understood and managed than 
the single force would have been. It is characteristic 
of great minds, to simplify these inquiries. They gain 
an insight into complicated and difficult subjects, not 
so much by any extraordinary faculty of seeing in the 
dark, as by the power of removing from the object all 
incidental causes of obscurity, until it shines in its own 
clear and simple light. 

If every force, when applied to a body, produces its 
full and legitimate effect, how many other forces soever 
may act upon it, impelling it different ways, then it 
must follow, that the smallest force ought to move the 


largest body ; and such is in fact the case. A snap of 
a finger upon a seventy-four under full sail, if applied 
in the direction of its motion, would actually increase 
its speed, although the effect might be too small to be 
visible. Still it is something, and may be truly ex- 
pressed by a fraction. Thus, suppose a globe, weigh- 
ing a million of pounds, were suspended from the ceil- 
ing by a string, and we should apply to it the snap of a 
finger, it is granted that the motion would be quite 
insensible. Let us then divide the body into a million 
equal parts, each weighing one pound ; then the same 
impulse, applied to each one separately, would produce 
a sensible effect, moving it, say one inch. It will be 
found, on trial, that the same impulse given to a mass 
of two pounds will move it half an inch ; and hence it is 
inferred, that, if applied to a mass weighing a million 
of pounds, it would move it the millionth part of an inch. 

It is one of the curious results of the second law of 
motion, that an unlimited number of motions may exist 
together in the same body. Thus, at the same moment^ 
we may be walking around a post in the cabin of a 
steam-boat, accompanying the boat in its passage around 
an island, revolving with the earth on its axis, flying 
through space in our annual circuit around the sun, and 
possibly wheeling, along with the sun and his whole 
retinue of planets, around some centre in common with 
the starry worlds. 

The THIRD LAW of motion is this : action and reac- 
tion are equal, and in contrary directions. 

Whenever I give a blow, the body struck exerts an 
equal force on the striking body. If I strike the water 
with an oar, the water communicates an equal impulse 
to the oar, which, being communicated to the boat, 
drives it forward in the opposite direction. If a magnet 
attracts a piece of iron, the iron attracts the magnet 
just as much, in the opposite direction ; and, in short, 
every portion of matter in the universe attracts and is 
attracted by every other, equally, in an opposite direc- 
tion. This brings us to the doctrine of universal gravi- 
12 L. A. 


tation, which is the very key that unlocks all the secrets 
of the skies. This will form the subject of my next 



" To Him no high, no low, no great, no small, 
He fills, He bounds, connects, and equals all." Pope. 

WE discover in Nature a tendency of every portion 
of matter towards every other. This tendency is called 
gravitation. In obedience to this power, a stone falls 
to the ground, and a planet revolves around the sun. 
We may contemplate this subject as it relates either 
to phenomena that take place near the surface of the 
earth, or in the celestial regions. The former, gravity, 
is exemplified by falling bodies ; the latter, universal 
gravitation, by the motions of the heavenly bodies. 
The laws of terrestrial gravity were first investigated by 
Galileo ; those of universal gravitation, by Sir Isaac 
Newton. Terrestrial gravity is only an individual ex- 
ample of universal gravitation ; being the tendency of 
bodies towards the centre of the earth. We are so 
much accustomed, from our earliest years, to see bodies 
fall to the earth, that we imagine bodies must of neces- 
sity fall " downwards ;" but when we reflect that the 
earth is round, and that bodies fall towards the centre 
on all sides of it, and that of course bodies on opposite 
sides of the earth fall in precisely opposite directions, 
and towards each other, we perceive that there must 
be some force acting to produce this effect ; nor is it 
enough to say, as the ancients did, that bodies " natur- 
ally" fall to the earth. Every motion implies some 
force which produces it ; and the fact that bodies fall 
towards the earth, on all sides of it, leads us to infer 
that that force, whatever it is, resides in the earth itself. 


We therefore call it attraction. We do not, however, 
say what attraction is, but what it does. We must bear 
in mind, also, that, according to the third law of mo- 
tion, this attraction is mutual ; that when a stone falls 
towards the earth, it exerts the same force on the earth 
that the earth exerts on the stone ; but the motion of 
the earth towards the stone is as much less than that of 
the stone towards the earth, as its quantity of matter is 
greater ; and therefore its motion is quite insensible. 

But although we are compelled to acknowledge the 
existence of such a force as gravity, causing a tendency 
in all bodies towards each other, yet we know nothing 
of its nature, nor can we conceive by what medium 
bodies at such a distance as the moon and the earth ex- 
ercise this influence on each other. Still, we may trace 
the modes in which this force acts ; that is, its laws ; 
for the laws of Nature are nothing else than the modes 
in which the powers of Nature act. 

We owe chiefly to the great Galileo the first investi- 
gation of the laws of terrestrial gravity, as exemplified 
in falling bodies ; and I will avail myself of this oppor- 
tunity to make you better acquainted with one of the 
most interesting of men and greatest of philosophers. 

Galileo was born at Pisa, in Italy, in the year 1564. 
He was the son of a Florentine nobleman, and was des- 
tined by his -father for the medical profession, and to 
this his earlier studies were devoted. But a fondness 
and a genius for mechanical inventions had developed 
itself, at a very early age, in the construction of his 
toys, and a love of drawing ; and as he grew older, a 
passion for mathematics, and for experimental research, 
predominated over his zeal for the study of medicine, 
and he fortunately abandoned that for the more conge- 
nial pursuits of natural philosophy and astronomy. In 
the twenty-fifth year of his age, he was appointed, by 
the Grand Duke of Tuscany, professor of mathematics 
in the University of Pisa. At that period, there pre- 
vailed in all the schools a most extraordinary reverence 
for the writings of Aristotle, the preceptor of Alexander 


the Great, a philosopher who flourished in Greece, 
about three hundred years before the Christian era. 
Aristotle, by his great genius and learning, gained a 
wonderful ascendency over the minds of men, and be- 
came the oracle of the whole reading world for twenty 
centuries. It was held, on the one hand, that all truths 
worth knowing were contained in the writings of Aris- 
totle ; and, on the other, that an assertion which con- 
tradicted any thing in Aristotle could not be true. But 
Galileo had a greatness of mind which soared above 
the prejudices of the age in which he lived, and dared 
to interrogate Nature by the two great and only suc- 
cessful methods of discovering her secrets, experiment 
and observation. Galileo was indeed the first philos- 
opher that ever fully employed experiments as the 
means of learning the laws of Nature, by imitating on 
a small what she performs on a great scale, and thus 
detecting her modes of operation. Archimedes, the 
great Sicilian philosopher, had in ancient times intro- 
duced mathematical or geometrical reasoning into nat- 
ural philosophy ; but it was reserved for Galileo to unite 
the advantages of both mathematical and experimental 
reasonings in the study of Nature, both sure and the 
only sure guides to truth, in this department of knowl- 
edge, at least. Experiment and observation furnish ma- 
terials upon which geometry builds her reasonings, and 
from which she derives many truths that either lie for 
ever hidden from the eye of observation, or which it 
would require ages to unfold. 

This method, of interrogating Nature by experiment 
and observation, was matured into a system by Lord 
Bacon, a celebrated English philosopher, early in the 
seventeenth century, indeed, during the life of Gali- 
leo. Previous to that time, the inquirers into Nature 
did not open their eyes to see how the facts really are ; 
but, by metaphysical processes, in imitation of Aristotle, 
determined how they ought to be, and hastily concluded 
that they were so. Thus, they did not study into the 
laws of motion, by observing how motion actually takes 


place, under various circumstances, but first, in their 
closets, constructed a definition of motion, and thence 
inferred all its properties. The system of reasoning re- 
specting the phenomena of Nature, introduced by Lord 
Bacon, was this : in the first place, to examine all the 
facts of the case, and then from these to determine the 
laws of Nature. To derive general conclusions from the 
comparison of a great number of individual instances 
constitutes the peculiarity of the Baconian philosophy. 
It is called the inductive system, because its conclusions 
were built on the induction, or comparison, of a great 
many single facts. Previous to the time of Lord Bacon, 
hardly any insight had been gained into the causes of 
natural phenomena, and hardly one of the laws of Na- 
ture had been clearly established, because all the in- 
quirers into Nature were upon a wrong road, groping 
their way through the labyrinth of error. Bacon point- 
ed out to them the true path, and held before them the 
torch-light of experiment and observation, under whose 
guidance all successful students of Nature have since 
walked, and by whose illumination they have gained so 
wonderful an insight into the- mysteries of the natural 

It is a remarkable fact, that two such characters as 
Bacon and Galileo should appear on the stage at the 
same time, who, without any communication with each 
other, or perhaps without any personal knowledge of 
each other's existence, should have each developed the 
true method of investigating the laws of Nature. Gali- 
leo practised what Bacon only taught ; and some, there- 
fore, with much reason, consider Galileo as a greater phi- 
losopher than Bacon. " Bacon," says Hume, " pointed 
out, at a great distance, the road to philosophy ; Galileo 
both pointed it out to others, and made, himself, consid- 
erable advances in it. The Englishman was ignorant 
of geometry ; the Florentine revived that science, ex- 
celled in it, and was the first who applied it, together 
with experiment, to natural philosophy. The former 
rejected, with the most positive disdain, the system of 


Copernicus : the latter fortified it with new proofs, de- 
rived both from reason and the senses." 

When we reflect that geometry is a science built 
upon self-evident truths, and that all its conclusions are 
the result of pure demonstration, and can admit of no 
controversy ; when we further reflect, that experimental 
evidence rests on the testimony of the senses, and we 
infer a thing to be true because we actually see it to be 
so ; it shows us the extreme bigotry, the darkness visi- 
ble, that beclouded the human intellect, when it not 
only refused to admit conclusions first established by 
pure geometrical reasoning, and afterwards confirmed 
by experiments exhibited in the light of day, but insti- 
tuted the most cruel persecutions against the great phi- 
losopher who first proclaimed these truths. Galileo 
was hated and persecuted by two distinct bodies of 
men, both possessing great influence in their respective 
spheres, the one consisting of the learned doctors of 
philosophy, who did nothing more, from age to age, 
than reiterate the doctrines of Aristotle, and were conse- 
quently alarmed at the promulgation of principles sub- 
versive of those doctrines ; the other consisting of the 
Romish priesthood, comprising the terrible Inquisition, 
who denounced the truths taught by Galileo, as incon- 
sistent with certain declarations of the Holy Scriptures. 
We shall see, as we advance, what a fearful warfare he 
had to wage against these combined powers of darkness. 

Aristotle had asserted, that, if two different weights 
of the same material were let fall from the same height, 
the heavier one would reach the ground sooner than 
the other, in proportion as it was more weighty. For 
example : if a ten-pound leaden weight and a one- 
pound were let fall from a given height at the same 
instant, the former would reach the ground ten times 
as soon as the latter. No one thought of making the 
trial, but it was deemed sufficient that Aristotle had 
said so ; and accordingly this assertion had long been 
received as an axiom in the science of motion. Galileo 
ventured to appeal from the authority of Aristotle to that 


of his own senses, and maintained, that both weights 
would fall in the same time. The learned doctors ridi- 
culed the idea. Galileo tried the experiment in their 
presence, by letting fall, at the same instant, large and 
small weights from the top of the celebrated leaning 
tower of Pisa. Yet, with the sound of the two weights 
clicking upon the pavement at the same moment, they 
still maintained that the ten-pound weight would reach 
the ground in one tenth part of the time of the other, 
because they could quote the chapter and verse of Aris- 
totle where the fact was asserted. Wearied and dis- 
gusted with the malice and folly of these Aristotelian 
philosophers, Galileo, at the age of twenty-eight, re- 
signed his situation in the university of Pisa, and remov- 
ed to Padua, in the university of which place he was 
elected professor of mathematics. Up to this period, 
Galileo had devoted himself chiefly to the studies of the 
laws of motion, and the other branches of mechanical 
philosophy. Soon afterwards, he began to publish his 
writings, in rapid succession, and became at once among 
the most conspicuous of his age, a rank which he 
afterwards well sustained and greatly exalted, by the 
invention of the telescope, and by his numerous astro- 
nomical discoveries. I will reserve an account of these 
great achievements until we come to that part of as- 
tronomy to which they were more immediately related, 
and proceed, now, to explain to you the leading prin- 
ciples of terrestrial gravity, as exemplified in falling 

First, all bodies near the earth's surface fall in 
straight lines towards the centre of the earth. We 
are not to infer from this fact, that there resides at the 
centre any peculiar force, as a great loadstone, for ex- 
ample, which attracts bodies towards itself ; but bodies 
fall towards the centre of the sphere, because the com- 
bined attractions of all the particles of matter in the 
earth, each exerting its proper force upon the body, 
would carry it towards the centre. This may be easily il- 
lustrated by a diagram. Let B, Fig. 29, page 140, be the 



centre of the earth, and A a body 
without it. Every portion of mat- 
ter in the earth exerts some force 
on A, to draw it down to the earth. 
But since there is just as much 
matter on one side of the line A B. 
as on the other side, each half ex- 
erts an equal force to draw the 
body towards itself; therefore it 
falls in the direction of the diago- 
nal between the two forces. Thus, 
if we compare the effects of any 
two particles of matter at equal distances from the line 
A B, but on opposite sides of it, as a, b, while the force 
of the particle at a would tend to draw A in the direc- 
tion of A a, that of b would draw it in the direction of 
A b, and it would fall in the line A B, half way be- 
tween the two. The same would hold true of any- 
other two corresponding particles of matter on differ- 
ent sides of the earth, in respect to a body situated in 
any place without it. 

Secondly, all bodies fall towards the earth, from 
the same height, with equal velocities. A musket-ball, 
and the finest particle of down, if let fall from a certain 
height towards the earth, tend to descend towards it at 
the same rate, and would proceed with equal speed, 
were it not for the resistance of the air, which retards 
the down more than it does the ball, and finally stops 
it. If, however, the air be removed out of the way, as 
it may be by means of the air-pump, the two bodies 
keep side by side in falling from the greatest height at 
which we can try the experiment. 

Thirdly, bodies, in falling towards the earth, have 
their rate of motion continually accelerated. Sup- 
pose we let fall a musket-ball from the top of a high 
tower, and watch its progress, disregarding the resist- 
ance of the air : the first second, it will pass over six- 
teen feet and one inch, but its speed will be constant- 
ly increased, being all the while urged onward by the 


same force, and retaining all that it has already acquir- 
ed ; so that the longer it is in falling, the swifter its 
motion becomes. Consequently, when bodies fall from 
a great height, they acquire an immense velocity be- 
fore they reach the earth. Thus, a man falling from a 
balloon, or from the mast-head of a ship, is broken in 
pieces ; and those meteoric stones, which sometimes 
fall from the sky, bury themselves deep in the earth. 
On measuring the spaces through which a body falls, 
it is found, that it will fall four times as far in two sec- 
onds as in one, and one hundred times as far in ten 
seconds as in one ; and universally, the space describ- 
ed by a falling body is proportioned to the time multi- 
plied into itself ; that is, to the square of the time. 

Fourthly, gravity is proportioned to the quantity of 
matter. A body which has twice as much matter as 
another exerts a force of attraction twice as great, and 
also receives twice as much from the same body as it 
would do, if it were only just as heavy as that body. 
Thus the earth, containing, as it does, forty times as 
much matter as the moon, exerts upon the moon forty 
times as much force as it would do, were its mass the 
same with that of the moon ; but it is also capable of 
receiving forty times as much gravity from the moon as 
it would do, were its mass the same as the moon's ; so 
that the power of attracting and that of being attracted 
are reciprocal ; and it is therefore correct to say, that 
the moon attracts the earth just as much as the earth 
attracts the moon ; arid the same may be said of any 
two bodies, however different in quantity of matter. 

Fifthly, gravity, when acting at a distance from 
the earth, is not as intense as it is near the earth. At 
such a distance as we are accustomed to ascend above 
the general level of the earth, no great difference is ob- 
served. On the tops of high mountains, we find bodies 
falling towards the earth, with nearly the same speed 
as they do from the smallest elevations. It is found, 
nevertheless, that there is a real difference ; so that, in 
fact, the weight of a body (which is nothing more 


than the measure of its force of gravity) is not quite 
so great on the tops of high mountains as at the general 
level of the sea. Thus, a thousand pounds' weight, on 
the top of a mountain half a mile high, would weigh 
a quarter of a pound less than at the level of the sea ; 
and if elevated four thousand miles above the earth, 
that is,, twice as far from the centre of the earth as the 
surface is from the centre, it would weigh only one 
fourth as much as before ; if three times as far, it would 
weigh only one ninth as much. So that the force of 
gravity decreases, as we recede from the earth, in the 
same proportion as the square of the distance increases. 
This fact is generalized by saying, that the force of 
gravity, at different distances from the earth, is in- 
versely as the square of the distance. 

Were a body to fall from a great distance, suppose a 
thousand times that of the radius of the earth, the force 
of gravity being one million times less than that at the 
surface of the earth, the motion of the body would be 
exceedingly slow, carrying it over only the sixth part 
of an inch in a day. It would be a long time, there- 
fore, in making any sensible approaches towards the 
earth ; but at length, as it drew near to the earth it 
would acquire a very great velocity, and would finally 
rush towards it with prodigious violence. Falling so 
far, and being continually accelerated on the way, we 
might suppose that it would at length attain a veloci- 
ty infinitely great ; but it can be demonstrated, that, 
if a body were to fall from an infinite distance, attract- 
ed to the earth only by gravity, it could never acquire 
a velocity greater than about seven miles per second. 
This, however, is a speed inconceivably great, being 
about eighteen times the greatest velocity that can be 
given to a cannon-ball, and more than twenty-five thous- 
and miles per hour. 

But the phenomena of falling bodies must have 
long been observed, and their laws had been fully in- 
vestigated by Galileo and others, before the cause of 
their falling was understood, or any such principle as 


gravity, inherent in the earth and in all bodies, was ap- 
plied to them. The developement of this great prin- 
ciple was the work of Sir Isaac Newton ; and I will 
give you, in my next Letter, some particulars respecting 
the life and discoveries of this wonderful man. 




" The heavens are all his own ; from the wild rule 
Of whirling vortices, and circling spheres, 
To their first great simplicity restored. 
The schools astonished stood ; but found it vain 
To combat long with demonstration clear, 
And, unawakened. dream beneath the blaze 
Of truth. At once their pleasing visions fled, 
With the light shadows of the morning mixed, 
When Newton rose, our philosophic sun." Thomson's Elegy. 

SIR ISAAC NEWTON was born in Lincolnshire, Eng- 
land, in 1642, just one year after the death of Galileo. 
His father died before he was born, and he was a help- 
less infant, of a diminutive size, and so feeble a frame, 
that his attendants hardly expected his life for a single 
hour. The family dwelling was of humble architec- 
ture, situated in a retired but beautiful valley, and was 
surrounded by a small farm, which afforded but a scanty 
living to the widowed mother and her precious charge. 
The cut on page 144, Fig 30, represents the modest 
mansion, and the emblems of rustic life that first met 
the eyes of this pride of the British nation, and orna- 
ment of human nature. It will probably be found, that 
genius has oftener emanated from the cottage than from 
the palace. 

The boyhood of Newton was distinguished chiefly for 
his ingenious mechanical contrivances. Among other 
pieces of mechanism, he constructed a windmill so cu- 
rious and complete in its workmanship, as to excite uni- 
versal admiration. After carrying it a while by the force 



Fig. 30. 

of the wind, he resolved to substitute animal power; 
and for this purpose he inclosed in it a mouse, which 
he called the miller, and which kept the mill a-going by 
acting on a tread-wheel. The power of the mouse 
was brought into action by unavailing attempts to 
reach a portion of corn placed above the wheel. A 
water-clock, a four-wheeled carriage propelled by the 
rider himself, and kites of superior workmanship, were 
among the productions of the mechanical genius of 
this gifted boy. At a little later period, he began to 
turn his attention to the motions of the heavenly bod- 
ies, and constructed several sun-dials on the walls of the 
house where he lived. All this was before he had 
reached his fifteenth year. At this age, he was sent 
by his mother, in company with an old family servant, 
to a neighboring market-town, to dispose of products 
of their farm, and to buy articles of merchandise for 
their family use ; but the young philosopher left all 
these negotiations to his worthy partner, occupying 
himself, mean-while, with a collection of old books, 
which he had found in a garret. At other times, he 
stopped on the road, and took shelter with his book 
under a hedge, until the servant returned. They en- 


deavored to educate him as a farmer ; but the perusal 
of a book, the construction of a water-mill, or some 
other mechanical or scientific amusement, absorbed all 
his thoughts, when the sheep were going astray, and 
the cattle were devouring or treading down the corn. 
One of his uncles having found him one day under a 
hedge, with a book in his hand, and entirely absorbed 
in meditation, took it from him, and found that it was 
a mathematical problem which so engrossed his atten- 
tion. His friends, therefore, wisely resolved to favor 
the bent of his genius, and removed him from the farm 
to the school, to prepare for the university. In the 
eighteenth year of his age, Newton was admitted into 
Trinity College, Cambridge. He made rapid and ex- 
traordinary advances in the mathematics, and soon af- 
forded unequivocal presages of that greatness which af- 
terwards placed him at the head of the human intellect. 
In 1669, at the age of twenty-seven, he became pro- 
fessor of mathematics at Cambridge, a post which he 
occupied for many years afterwards. During the four 
or five years previous to this he had, in fact, made most 
of those great discoveries which have immortalized his 
name. We are at present chiefly interested in one of 
these, namely, that of universal gravitation; and let 
us see by what steps he was conducted to this greatest 
of scientific discoveries. 

In the year 1666, when Newton was about twenty- 
four years of age, the plague was prevailing at Cam- 
bridge, and he retired into the country. One day, while 
he sat in a garden, musing on the phenomena of Nature 
around him, an apple chanced to fall to the ground. Re- 
flecting on the mysterious power that makes all bodies 
near the earth fall towards its centre, and considering 
that this power remains unimpaired at considerable 
heights above the earth, as on the tops of trees and moun- 
tains, he asked himself, " May not the same force ex- 
tend its influence to a great distance from the earth, even 
as far as the moon ? Indeed, may not this be the very 
reason, why the moon is drawn away continually from 
13 L. A. 


the straight line in which every body tends to move, and 
is thus made to circulate around the earth ?" You will 
recollect that it was mentioned, in my Letter which con- 
tained an account of the first law of motion, that if a 
body is put in motion by any force, it will always move 
forward in a straight line, unless some other force com- 
pels it to turn aside from such a direction ; and that, when 
we see a body moving in a curve, as a circular orbit, we 
are authorized to conclude that there is some force ex- 
isting within the circle, which continually draws the 
body away from the direction in which it tends to move. 
Accordingly, it was a very natural suggestion, to one 
so well acquainted with the laws of motion as Newton, 
that the moon should constantly bend towards the earth, 
from a tendency to fall towards it, as any other heavy 
body would do, if carried to such a distance from the 
earth. Newton had already proved, that if such a pow- 
er as gravity extends from the earth to distant bodies, it 
must decrease, as the square of the distance from the 
centre of the earth increases ; that is, at double the dis- 
tance, it would be four times less ; at ten times the dis- 
tance, one hundred times less ; and so on. Now, it 
was known that the moon is about sixty times as far 
from the centre of the earth as the surface of the earth 
is from the centre, and consequently, the force of attrac- 
tion at the moon must be the square of sixty, or thirty-six 
hundred times less than it is at the earth ; so that a body 
at the distance of the moon would fall towards the 
earth very slowly, only one thirty-six hundredth part as 
far in a given time, as at the earth. Does the moon ac- 
tually fall towards the earth at this rate ; or, what is the 
same thing, does she depart at this rate continually from 
the straight line in which she tends to move, and in 
which she would move, if no external force diverted her 
from it ? On making the calculation, such was found 
to be the fact. Hence gravity, and no other force than 
gravity, acts upon the moon, and compels her to revolve 
around the earth. By reasonings equally conclusive, it 
was afterwards proved, that a similar force compels all 


the planets to circulate around the sun ; and now, we 
may ascend from the contemplation of this force, as we 
have seen it exemplified in falling bodies, to that of a 
universal power whose influence extends to all the ma- 
terial creation. It is in this sense that we recognise the 
principle of universal gravitation, the law of which may 
be thus enunciated ; all bodies in the universe, wheth- 
er great or small, attract each other, with forces pro- 
portioned to their respective quantities of matter, and 
inversely as the squares of their distances from each 

This law asserts, first, that attraction reigns through- 
out the material world, affecting alike the smallest par- 
ticle of matter and the greatest body ; secondly, that 
it acts upon every mass of matter, precisely in propor- 
tion to its quantity ; and, thirdly, that its intensity is di- 
minished as the square of the distance is increased. 

Observation has fully confirmed the prevalence of this 
law throughout the solar system ; and recent discoveries 
among the fixed stars, to be more fully detailed hereaf- 
ter, indicate that the same law prevails there. The law 
of universal gravitation is therefore held to be the grand 
principle which governs all the celestial motions. Not 
only is it consistent with all the observed motions of the 
heavenly bodies, even the most irregular of those mo- 
tions, but, when followed out into all its consequences, 
it would be competent to assert that such irregularities 
must take place, even if they had never been observed. 

Newton first published the doctrine of universal grav- 
itation in the ' Principia,' in 1687. The name implies 
that the work contains the fundamental principles of 
natural philosophy and astronomy. Being founded up- 
on the immutable basis of mathematics, its conclusions 
must of course be true and unalterable, and thenceforth 
we may regard the great laws of the universe as traced 
to their remotest principle. The greatest astronomers 
and mathematicians have since occupied themselves in 
following out the plan which Newton began, by applying 
the principles of universal gravitation to all the subordi- 


nate as well as to the grand movements of the spheres. 
This great labor has been especially achieved by La 
Place, a French mathematician of the highest eminence, 
in his profound work, the ' Mecanique Celeste.' Of this 
work, our distinguished countryman, Dr. Bowditch, has 
given a magnificent translation, and accompanied it with 
a commentary, which both illustrates the original, and 
adds a great amount of matter hardly less profound 
than that. 

We have thus far taken the earth's orbit around the 
sun as a great circle, such being its projection on the 
sphere constituting the celestial ecliptic. The real path 
of the earth around the sun is learned, as I before ex- 
plained to you, by the apparent path of the sun around 
the earth once a year. Now, when a body revolves 
about the earth at a great distance from us, as is the 
case with the sun and moon, we cannot certainly infer 
that it moves in a circle because it appears to describe 
a circle on the face of the sky, for such might be the 
appearance of its orbit, were it ever so irregular a curve. 
Thus, if E, Fig. 31, represents the earth, and A CB, 

Fig. 31. 

the irregular path of a body revolving about it, since we 
should refer the body continually to some place on the 
celestial sphere, X Y Z, determined by lines drawn 
from the eye to the concave sphere through the body, 



the body, while moving from A to B through C, would 
appear to move from X to Z, through Y. Hence, we 
must determine from other circumstances than the actual 
appearance, what is the true figure of the orbit. 

Were the earth's path a circle, having the sun in the 
centre, the sun would always appear to be at the same 
distance from us ; that is, the radius of the orbit, or ra- 
dius vector., (the name given to a line drawn from 
the centre of the sun to the orbit of any planet,) would 
always be of the same length. But the earth's distance 
from the sun is constantly varying, which shows that 
its orbit is not a circle. We learn the true figure of 
the orbit, by ascertaining the relative distances of the 
earth from the sun, at various periods of the year. 
These distances all being laid down in a diagram, ac- 
cording to their respective lengths, the extremities, on 
being connected, give us our first idea of the shape of 
the orbit, which appears of an oval form, and at least 
resembles an ellipse ; and, on further trial, we find 
that it has the properties of an ellipse. Thus, let E, 
Fig. 32, be the place of the earth, and o, 6, c, &c., suc- 

Fig. 32. 

cessive positions of the sun ; the relative lengths of the 
lines E a, E 6, &c., being known, on connecting the 


points a, &, c, &c., the resulting figure indicates the 
true figure of the earth's orbit. 

These relative distances are found in two different 
ways ; first, by changes in the sun's apparent diameter. 
and, secondly, by variations in his angular velocity. 
The same object appears to us smaller in proportion as 
it is more distant ; and if we see a heavenly body vary- 
ing in size, at different times, we infer that it is at dif- 
ferent distances from us ; that when largest, it is near- 
est to us, and when smallest, furthest off. Now, when 
the sun's diameter is accurately measured by instru- 
ments, it is found to vary from day to day ; being, 
when greatest, more than thirty-two minutes and a 
half, and when smallest, only thirty-one minutes and 
a half, differing, in all, about seventy-five seconds. 
When the diameter is greatest, which happens in Jan- 
uary, we know that the sun is nearest to us ; and when 
the diameter is least, which occurs in July, we infer that 
the sun is at the greatest distance from us. The point 
where the earth, or any planet, in its revolution, is near- 
est the sun, is called its perihelion ; the point where it 
is furthest from the sun, its aphelion. Suppose, then, 
that, about the first of January, when the diameter of 
the sun is greatest, we draw a line, E a, Fig, 32, to 
represent it, and afterwards, every ten days, draw other 
lines, E b, E c, &c. ; increasing in the same ratio as 
the apparent diameters of the sun decrease. These 
lines must be drawn at such a distance from each oth- 
er, that the triangles, E a b, E b c, &c., shall be all equal 
to each other, for a reason that will be explained here- 
after. On connecting the extremities of these lines, we 
shall obtain the figure of the earth's orbit. 

Similar conclusions may be drawn from observations 
on the sun's angular velocity. A body appears to 
move most rapidly when nearest to us. Indeed, the 
apparent velocity increases rapidly, as it approaches us, 
and as rapidly diminishes, when it recedes from us. If 
it comes twice as near as before, it appears to move not 
merely twice as swiftly, but four times as swiftly ; if it 


comes ten times nearer, its apparent velocity is one hun- 
dred times as great as before. We say, therefore, that 
the velocity varies inversely as the square of the dis- 
tance ; for, as the distance is diminished ten times, the 
velocity is increased the square of ten ; that is, one hun- 
dred times. Now, by noting the time it takes the sun, 
from day to day, to cross the central wire of the transit- 
instrument, we learn the comparative velocities with 
which it moves at different times ; and from these we 
derive the comparative distances of the sun at the cor- 
responding times ; and laying down these relative dis- 
tances in a diagram, as before, we get our first notions 
of the actual figure of the earth's orbit, or the path 
which it describes in its annual revolution around the 

Having now learned the fact, that the earth moves 
around the sun, not in a circular but in an elliptical 
orbit, you will desire to know by what forces it is im- 
pelled, to make it describe this figure, with such unifor- 
mity and constancy, from age to age. It is commonly 
said, that gravity causes the earth and the planets to 
circulate around the sun ; and it is true that it is gravi- 
ty which turns them aside from the straight line in 
which, by the first law of motion, they tend to move, 
and thus causes them to revolve around the sun. But 
what force is that which gave to them this original im- 
pulse, and impressed upon them such a tendency to 
move forward in a straight line ? The name projectile 
force is given to it, because it is the same as though the 
earth were originally projected into space, when first 
created ; and therefore its motion is the result of two 
forces, the projectile force, which would cause it to 
move forward in a straight line which is a tangent to 
its orbit, and gravitation, which bends it towards the 
sun. But before you can clearly understand the nature 
of this motion, and the action of the two forces that 
produce it, I must explain to you a few elementary 
principles upon which this and all the other planetary 
motions depend. 


You have already learned, that when a body is act- 
ted on by two forces, in different directions, it moves 
in the direction of neither, but in some direction be- 
tween them. If I throw a stone horizontally, the at- 
traction of the earth will continually draw it downward, 
out of the line of direction in which it was thrown, and 
make it descend to the earth in a curve. The particu- 
lar form of the curve will depend on the velocity with 
which it is thrown. It will always begin to move in 
the line of direction in which it is projected; but it 
will soon be turned from that line towards the earth. It 
will, however, continue nearer to the line of projection 
in proportion as the velocity of projection is greater. 
Thus, let A C, Fig. 33, be perpendicular to the horizon, 

Fig. 33. 

and A B parallel to it, and let a stone be thrown from 
A, in the direction of A B. It will, in every case, com- 
mence its motion in the line A B, which will therefore 
be a tangent to the curve it describes ; but, if it is thrown 
with a small velocity, it will soon depart from the tan- 
gent, describing the line A D ; with a greater velocity, 
it will describe a curve nearer the tangent, as A E ; and 
with a still greater velocity, it will describe the curve 

As an example of a body revolving in an orbit i*.. 
the influence of two forces, suppose a body placv 
any point, P, Fig. 34, above the surface of the earth, 
and let P A be the direction of the earth's centre ; that 
is, a line perpendicular to the horizon. If the body 
were allowed to move, without receiving any impulse, 


it would descend to the earth in the direction P A with 
an accelerated motion. But suppose that, at the mo- 
ment of its departure from P, it receives a blow in the 
direction P B, which would carry it to B in the time the 
body would fall from P to A ; then, under the influence 
of both forces, it would descend along the curve P D. 
If a stronger blow were given to it in the direction P B, 
it would describe a larger curve, P E ; or, finally, if 
the impulse were sufficiently strong, it would circulate 
quite around the earth, and return again to P, describ- 
ing the circle P F G. With a velocity of projection 
still greater, it would describe an ellipse, P I K ; and if 
the velocity be increased to a certain degree, the figure 
becomes a parabola, L P M, a curve which never re- 
turns into itself. 

In Fig. 35, page 154, suppose the planet to have passed 
the point C, at the aphelion, with so small a velocity, that 
the attraction of the sun bends its path very much, and 
onuses it immediately to begin to approach towards the 
~$ftf, r The sun's attraction will increase its velocity, as 
K tg^ves through D, E, and F, for the sun's attractive 
force" on the planet, when at D, is acting in the direction 
D S ; and, on account of the small angle made between 
D E and D S, the force acting in the line D S helps the 
planet forward in the path D E, and thus increases its 




Fi S- 35 - velocity. In like manner, 

the velocity of the planet 
will be continually increas- 
ing as it passes through D, 
E, and F ; and though the 
attractive force, on account 
of the planet's nearness, is 
so much increased, and 
tends, therefore, to make 
the orbit more curved, yet 
the velocity is also so much 
increased, that the orbit is 
not more curved than be- 
fore ; for the same increase 
of velocity, occasioned by the planet's approach to the 
sun, produces a greater increase of centrifugal force, 
which carries it off again. We may see, also, the rea- 
son why, when the planet has reached the most distant 
parts of its orbit, it does not entirely fly off, and never 
return to the sun ; for, when the planet passes along 
H, K, A, the sun's attraction retards the planet, just as 
gravity retards a ball rolled up hill ; and when it has 
reached C, its velocity is very small, and the attraction 
to the centre of force causes a great deflection from the 
tangent, sufficient to give its orbit a great curvature, and 
the planet wheels about, returns to the sun, and goes 
over the same orbit again. As the planet recedes from 
the sun, its centrifugal force diminishes faster than the , 
force of gravity, so that the latter finally preponderates, a 
I shall conclude what I have to say at present, respect- <j 
ing the motion of the earth around the sun, by adding 
a few words respecting the precession of the equinoxes. 
The precession of the equinoxes is a slow but con- 
tinual shifting of the equinoctial points, from east to 
west. Suppose that we mark the exact place in the 
heavens where, during the present year, the sun crosses 
the equator, and that this point is close to a certain star ; 
next year, the sun will cross the equator a little way west- 
ward of that star, and so every year, a little further west- 


ward, until, in a long course of ages, the place of the 
equinox will occupy successively every part of the eclip- 
tic, until we come round to the same star again. As, 
therefore, the sun revolving from west to east, in his ap- 
parent orbit, comes round to the point where it left the 
equinox, it meets the equinox before it reaches that 
point. The appearance is as though the equinox goes 
forward to meet the sun, and hence the phenomenon 
is called the precession of the equinoxes ; and the fact 
is expressed by saying, that the equinoxes retrograde on 
the ecliptic, until the line of the equinoxes (a straight 
line drawn from one equinox to the other) makes a com- 
plete revolution, from east to west. This is of course 
a retrograde motion, since it is contrary to the order of 
the signs. The equator is conceived as sliding west- 
ward on the ecliptic, always preserving the same in- 
clination to it, as a ring, placed at a small angle with 
another of nearly the same size which remains fixed, 
may be slid quite around it, giving a corresponding mo- 
tion to the two points of intersection. It must be ob- 
served, however, that this mode of conceiving of the 
precession of the equinoxes is purely imaginary, and is 
employed merely for the convenience of representation. 

The amount of precession annually is fifty seconds 
and one tenth ; whence, since there are thirty-six hun- 
dred seconds in a degree, and three hundred and six- 
ty degrees in the whole circumference of the ecliptic, 
and consequently one million two hundred and ninety- 
-ix thousand seconds, this sum, divided by fifty seconds 
.nd one tenth, gives twenty-five thousand eight hundred 
and sixty-eight years for the period of a complete revo- 
lution of the equinoxes. 

Suppose we now fix to the centre of each of the two 
rings, before mentioned, a wire representing its axis, one 
corresponding to the axis of the ecliptic, the other to 
that of the equator, the extremity of each being the pole 
of its circle. As the ring denoting the equator turns 
round on the ecliptic, which, with its axis, remains fixed, 
it is easy to conceive that the axis of the equator revolves 


around that of the ecliptic, and the pole of the equator 
around the pole of the ecliptic, and constantly at a dis- 
tance equal to the inclination of the two circles. To 
transfer our conceptions to the celestial sphere, we may 
easily see that the axis of the diurnal sphere (that of the 
earth produced) would not have its pole constantly in 
the same place among the stars, but that this pole would 
perform a slow revolution around the pole of the eclip- 
tic, from east to west, completing the circuit in about 
twenty-six thousand years. Hence the star which we 
now call the pole-star has not always enjoyed that dis- 
tinction, nor will it always enjoy it, hereafter. When 
the earliest catalogues of the stars were made, this star 
was twelve degrees from the pole. It is now one degree 
twenty-four minutes, and will approach still nearer ; or, 
to speak more accurately, the pole will come still near- 
er to this star, after which it will leave it, and success- 
ively pass by others. In about thirteen thousand years, 
the bright star Lyra (which lies near the circle in which 
the pole of the equator revolves about the pole of the 
ecliptic, on the side opposite to the present pole-star) 
will be within five degrees of the pole, and will consti- 
tute the pole-star. As Lyra now passes near our zenith, 
you might suppose that the change of position of the 
pole among the stars would be attended with a change 
of altitude of the north pole above the horizon. This 
mistaken idea is one of the many misapprehensions 
which result from the habit of considering the horizon 
as a fixed circle in space. However the pole might 
shift its position in space, we should still be at the same 
distance from it, and our horizon would always reach the 
same distance beyond it. 

The time occupied by the sun, in passing from the 
equinoctial point round to the same point again, is call- 
ed the tropical year. As the sun does not perform a 
complete revolution in this interval, but falls short of it 
fifty seconds and one tenth, the tropical year is shorter 
than the sidereal by twenty minutes and twenty sec- 
onds, in mean solar time, this being the time of describ- 

THE MOON. 157 

ing an arc of fifty seconds and one tenth, in the annual 

The changes produced by the precession of the equi- 
noxes, in the apparent places of the circumpolar stars, 
have led to some interesting results in chronology. In 
consequence of the retrograde motion of the equinoc- 
tial points, the signs of the ecliptic do not correspond, 
at present, to the constellations which bear the same 
names, but lie about one sign, or thirty degrees, west- 
ward of them. Thus, that division of the ecliptic which 
is called the sign Taurus lies in the constellation Aries, 
and the sign Gemini, in the constellation Taurus. Un- 
doubtedly, however, when the ecliptic was thus first di- 
vided, and the divisions named, the several constella- 
tions lay in the respective divisions which bear their 



14 Soon as the evening shades prevail 
The Moon takes up the wondrous tale, 
And nightly to the listening earth 
Repeats the story of her birth." Addison. 

HAVING now learned so much of astronomy as re- 
lates to the earth and the sun, and the mutual relations 
which exist between them, you are prepared to enter 
with advantage upon the survey of the other bodies that 
compose the solar system. This being done, we shall 
then have still before us the boundless range of the 
fixed stars. 

The moon, which next claims our notice, has been 
studied by astronomers with greater attention than any 
other of the heavenly bodies, since her comparative 
nearness to the earth brings her peculiarly within the 
range of our telescopes, and her periodical changes and 
very irregular motions, afford curious subjects, both for 
observation and speculation. The mild light of the 

14 L. A. 


moon also invites our gaze, while her varying aspects 
serve barbarous tribes, especially, for a kind of dial- 
plate inscribed on the face of the sky, for weeks, and 
months, and times, and seasons. 

The moon is distant from the earth about two hun- 
dred and forty thousand miles ; or, more exactly, two 
hundred and thirty-eight thousand five hundred and 
forty-five miles. Her angular or apparent diameter is 
about half a degree, and her real diameter, two thous- 
and one hundred and sixty miles. She is a compan- 
ion, or satellite, to the earth, revolving around it every 
month, and accompanying us in our annual revolution 
around the sun. Although her nearness to us makes 
her appear as a large and conspicuous object in the 
heavens, yet, in comparison with most of the other ce- 
lestial bodies, she is in fact very small, being only one 
forty-ninth part as large as the earth, and only about one 
seventy millionth part as large as the sun. 

The moon shines by light borrowed from the sun, 
being itself an opaque body, like the earth. When the 
disk, or any portion of it, is illuminated, we can plainly 
discern, even with the naked eye, varieties of light and 
shade, indicating inequalities of surface which we im- 
agine to be land and water. I believe it is the common 
impression, that the darker portions are land and the 
lighter portions water; but if either part is water, it 
must be the darker regions. A smooth polished sur- 
face, like water, would reflect the sun's light like a mir- 
ror. It would, like a convex mirror, form a diminished 
image of the sun, but would not itself appear luminous 
like an uneven surface, which multiplies the light by 
numerous reflections within itself. Thus, from this 
cause, high broken mountainous districts appear more 
luminous than extensive plains. 

By the aid of the telescope, we may see undoubted 
indications of mountains and valleys. Indeed, with a 
good glass, we can discover the most decisive evidence 
that the surface of the moon is exceedingly varied, 
one part ascending in lofty peaks, another clustering in 

Figures 36, 37. 


THE MOON. 159 

huge mountain groups, or long ranges, and another 
bearing all the marks of deep caverns or valleys. You 
will not, indeed, at the first sight of the moon through 
a telescope, recognise all these different objects. If 
you look at the moon when half her disk is enlight- 
ened, (which is the best time for seeing her varieties 
of surface,) you will, at the first glance, observe a mot- 
ley appearance, particularly along the line called the 
terminator, which separates the enlightened from the 
unenlightened part of the disk. (Fig. 37.) On one 
side of the terminator, within the dark part of the 
disk, you will see illuminated points, and short, crooked 
lines, like rude characters marked with chalk on a black 
ground. On the other side of the terminator you will 
see a succession of little circular groups, appearing like 
numerous bubbles of oil on the surface of water. The 
further you carry your eye from the terminator, on the 
same side of it, the more indistinctly formed these bub- 
bles appear, until towards the edge of the moon they 
assume quite a different aspect. 

Some persons, when they look into a telescope for 
the first time, having heard that mountains and valleys 
are to be seen, and discovering nothing but these un- 
meaning figures, break off in disappointment, and have 
their faith in these things rather diminished than in- 
creased. I would advise you, therefore, before you 
take even your first view of the moon through a teles- 
cope, to form as clear an idea as you can, how moun- 
tains, and valleys, and caverns, situated at such a dis- 
tance from the eye, ought to look, and by what marks 
they may be recognised. Seize, if possible, the most 
favorable period, (about the time of the first quarter,) 
and previously learn from drawings and explanations, 
how to interpret every thing you see. 

What, then, ought to be the respective appearances 
of mountains, valleys, and deep craters, or caverns, in 
the moon ? The sun shines on the moon in the same 
way as it shines on the earth ; and let us reflect, then, 
upon the manner in which it strikes similar objects here. 


One half the globe is constantly enlightened ; and, by 
the revolution of the earth on its axis, the terminator, 
or the line which separates the enlightened from the 
unenlightened part of the earth, travels along from 
east to west, over different places, as we see the moon's 
terminator travel over her disk from new to full moon ; 
although, in the case of the earth, the motion is more 
rapid, and depends on a different cause. In the morn- 
ing, the sun's light first strikes upon the tops of the 
mountains, and, if they are very high, they may be 
brightly illuminated while it is yet night in the valleys 
below. By degrees, as the sun rises, the circle of illu- 
mination travels down the mountain, until at length it 
reaches the bottom of the valleys ; and these in turn 
enjoy the full light of day. Again, a mountain casts a 
shadow opposite to the sun, which is very long when 
the sun first rises, and shortens continually as the sun 
ascends, its length at a given time, however, being pro- 
portioned to the height of the mountain ; so that, if the 
shadow be still very long when the sun is far above the 
horizon, we infer that the mountain is very lofty. We 
may, moreover, form some judgement of the shape of 
a mountain, by observing that of its shadow. 

Now, the moon is so distant that we could not easily 
distinguish places simply by their elevations, since they 
would be projected into the same imaginary plane which 
constitutes the apparent disk of the moon ; but the fore- 
going considerations would enable us to infer their ex- 
istence. Thus, when you view the moon at any time 
within her first quarter, but better near the end of that 
period, you will observe, on the side of the terminator 
within the dark part of the disk, the tops of moun- 
tains which the light of the sun is just striking, as the 
morning sun strikes the tops of mountains on the earth. 
These you will recognise by those white specks and 
little crooked lines, before mentioned, as is represent- 
ed in Fig. 37. These bright points and lines you will 
see altering their figure, every hour, as they come 
more and more into the sun's light; and, mean-while. 

THE MOON. 161 

other bright points, very minute at first, will start into 
view, which also in turn grow larger as the termi- 
nator approaches them, until they fall into the enlight- 
ened part of the disk. As they fall further and further 
within this part, you will have additional proofs that 
they are mountains, from the shadows which they cast 
on the plain, always in a direction opposite to the sun. 
The mountain itself may entirely disappear, or become 
confounded with the other enlightened portions of the 
surface ; but its position and its shape may still be rec- 
ognised by the dark line which it projects on the plane. 
This line will correspond in shape to that of the moun- 
tain, presenting at one time a long serpentine stripe of 
black, denoting that the mountain is a continued range ; 
at another time exhibiting a conical figure tapering to a 
point, or a series of such sharp points ; or a serrated, un- 
even termination, indicating, in each case respectively, 
a conical mountain, or a group of peaks, or a range with 
lofty cliffs. All these appearances will indeed be seen 
in miniature ; but a little familiarity with them will en- 
able you to give them, in imagination, their proper di- 
mensions, as you give to the pictures of known animals 
their due sizes, although drawn on a scale far below 
that of real life. 

In the next place, let us see how valleys and deep 
craters in the moon might be expected to appear. We 
could not expect to see depressions any more than ele- 
vations, since both would alike be projected on the same 
imaginary disk. But we may recognise such depres- 
sions, from the manner in which the light of the sun 
shines into them. When we hold a china tea-cup at 
some distance from a candle, in the night, the candle be- 
ing elevated but little above the level of the top of the 
cup, a luminous crescent will be formed on the side of 
the cup opposite to the candle, while the side next to the 
candle will be covered by a deep shadow. As we grad- 
ually elevate the candle, the crescent enlarges and travels 
down the side of the cup, until finally the whole interior 
becomes illuminated. We observe similar appearances 


in the moon, which we recognise as deep depressions. 
They are those circular spots near the terminator before 
spoken of, which look like bubbles of oil floating on 
water. They are nothing else than circular craters or 
deep valleys. When they are so situated that the light 
of the sun is just beginning to shine into them, you may 
see, as in the tea-cup, a luminous crescent around the 
side furthest from the sun, while a deep black shadow 
is cast on the side next to the sun. As the cavity is 
turned more and more towards the light, the crescent 
enlarges, until at length the whole interior is illuminat- 
ed. If the tea-cup be placed on a table, and a candle 
be held at some distance from it, nearly on a level with 
the top, but a little above it, the cup itself will cast 
a shadow on the table, like any other elevated object 
In like manner, many of these circular spots on the 
moon cast deep shadows behind them, indicating that, 
the tops of the craters are elevated far above the gen- 
eral level of the moon. The regularity of some of 
these circular spots is very remarkable. The circle, in 
some instances, appears as well formed as could be de- 
scribed by a pair of compasses, while in the centre there 
not unfrequently is seen a conical mountain casting its 
pointed shadow on the bottom of the crater. I hope 
you will enjoy repeated opportunities to view the moon 
through a telescope. Allow me to recommend to you, 
not to rest satisfied with a hasty or even with a single 
view, but to verify the preceding remarks by repeated 
and careful inspection of the lunar disk, at different ages 
of the moon. 

The various places on the moon's disk have received 
appropriate names. The dusky regions being formerly 
supposed to be seas, were named accordingly ; and other 
remarkable places have each two names, one derived 
from some well-known spot on the earth, and the other 
from some distinguished personage. Thus, the same 
bright spot on the surface of the moon is called Mount 
Sinai or Tycho, and another, Mount Etna or Coper- 
nicus. The names of individuals, however, are more 

THE MOON. 163 

used than the others. The diagram, Fig. 36, (see page 
159,) represents rudely, the telescopic appearance of 
the full moon. The reality is far more beautiful. A 
few of the most remarkable points have the following 
names corresponding to the numbers and letters on the 

1. Tycho, 6. Eratosthenes, 

2. Kepler, 7. Plato, 

3. Copernicus, 8. Archimedes, 

4. Aristarchus, 9. Eudoxus, 

5. Helicon, 10. Aristotle. 

A. Mare Humorum, Sea of Humors, 

B. Mare Nubium, Sea of Clouds, 

C. Mare Imbrium, Sea of Rains, 

D. Mare Nectaris, Sea of Nectar, 

E. Mare Tranquillitatis, Sea of Tranquillity) 

F. Mare Serenitatis, Sea of Serenity, 

G. Mare Fecunditatis, Sea of Plenty, 
H. Mare Crisium, Crisian Sea. 

The heights of the lunar mountains, and the depths 
of the valleys, can be estimated with a considerable de- 
gree of accuracy. Some of the mountains are as high 
as five miles, and the valleys, in some instances, are four 
miles deep. Hence it is inferred, that the surface of 
the moon is more broken and irregular than that of the 
earth, its mountains being higher and its valleys deeper, 
in proportion to its magnitude, than those of the earth. 

The varieties of surface in the moon, as seen by the 
aid of large telescopes, have been well described by 
Dr. Dick, in his ( Celestial Scenery,' and I cannot give 
you a better idea of them, than to add a few extracts 
from his work. The lunar mountains in general exhibit 
an arrangement and an aspect very different from the 
mountain scenery of our globe. They may be arrang- 
ed under the four following varieties : 

First, insulated mountains, which rise from plains 
nearly level, shaped like a sugar loaf, which may be 
supposed to present an appearance somewhat similar 


to Mount Etna, or the Peak of TenerifTe. The shad- 
ows of these mountains, in certain phases of the moon, 
are as distinctly perceived as the shadow of an upright 
staff, when placed opposite to the sun ; and these heights 
can be calculated from the length of their shadows. 
Some of these mountains being elevated in the midst of 
extensive plains, would present to a spectator on their 
summits magnificent views of the surrounding regions. 

Secondly, mountain ranges, extending in length two 
or three hundred miles. These ranges bear a distant re- 
semblance to our Alps, Apennines, and Andes ; but they 
are much less in extent. Some of them appear very 
rugged and precipitous ; and the highest ranges are in 
some places more than four miles in perpendicular alti- 
tude. In some instances, they are nearly in a straight 
line from northeast to southwest, as in the range called 
the Apennines ; in other cases, they assume the form of 
a semicircle, or crescent. 

Thirdly, circular ranges, which appear on almost 
every part of the moon's surface, particularly in its south- 
ern regions. This is one grand peculiarity of the lunar 
ranges, to which we have nothing similar on the earth. 
A plain, and sometimes a large cavity, is surrounded 
with a circular ridge of mountains, which encompasses 
it like a mighty rampart. These annular ridges and 
plains are of all dimensions, from a mile to forty or fifty 
miles in diameter, and are to be seen in great numbers 
over every region of the moon's surface ; they are most 
conspicuous, however, near the upper and lower limbs, 
about the time of the half moon. 

The mountains which form these circular ridges are 
of different elevations, from one fifth of a mile to three 
miles and a half, and their shadows cover one half of the 
plain at the base. These plains are sometimes on a lev- 
el with the general surface of the moon, and in other 
cases they are sunk a mile or more below the level of 
the ground which surrounds the exterior circle of the 

Fourthly, central mountains, or those which are plac- 

THE MOON. 165 

ed in the middle of circular plains. In many of the plains 
and cavities surrounded by circular ranges of mountains 
there stands a single insulated mountain, which rises 
from the centre of the plain, and whose shadow some- 
times extends, in the form of a pyramid, half across 
the plain to the opposite ridges. These central moun- 
tains are generally from half a mile to a mile and a half 
in perpendicular altitude. In some instances, they have 
two, and sometimes three, different tops, whose shad- 
ows can be easily distinguished from each other. Some- 
times they are situated towards one side of the plain, or 
cavity ; but in the great majority of instances their po- 
sition is nearly or exactly central. The lengths of their 
bases vary from five to about fifteen or sixteen miles. 
The lunar caverns form a very peculiar and promi- 
nent feature of the moon's surface, and are to be seen 
throughout almost every region, but are most numerous 
in the southwest part of the moon. Nearly a hundred 
of them, great and small, may be distinguished in that 
quarter. They are all nearly of a circular shape, and 
appear like a very shallow egg-cup. The smaller cav- 
ities appear, within, almost like a hollow cone, with the 
sides tapering towards the centre ; but the larger ones 
have, for the most part, flat bottoms, from the centre 
of which there frequently rises a small, steep, conical 
hill, which gives them a resemblance to the circular 
ridges and central mountains before described. In 
some instances, their margins are level with the gene- 
ral surface of the moon ; but, in most cases, they are en- 
circled with a high annular ridge of mountains, marked 
with lofty peaks. Some of the larger of these cavities 
contain smaller cavities of the same kind and form, par- 
ticularly in their sides. The mountainous ridges which 
surround these cavities reflect the greatest quantity of 
light ; and hence that region of the moon in which they 
abound appears brighter than any other. From their 
lying in every possible direction, they appear, at and 
near the time of full moon, like a number of brilliant 
streaks, or radiations. These radiations appear to con- 


verge towards a large brilliant spot, surrounded by a 
faint shade, near the lower part of the moon, which is 
named Tycho, a spot easily distinguished even by a 
small telescope. The spots named Kepler and Coper- 
nicus are each composed of a central spot with lumin- 
ous radiations.* 

The broken surface and apparent geological struc- 
ture of the moon has suggested the opinion, that the 
moon has been subject to powerful volcanic action. 
This opinion receives support from certain actual ap- 
pearances of volcanic fires, which have at different 
times been observed. In a total eclipse of the sun, the 
moon comes directly between us and that luminary, and 
presents her dark side towards us under circumstances 
very favorable for observation. At such times, several 
astronomers, at different periods, have noticed bright 
spots, which they took to be volcanoes. It must evi- 
dently require a large fire to be visible at all, at such a 
distance ; and even a burning spark, or point but just 
visible in a large telescope, might be in fact a volcano 
raging like Etna or Vesuvius. Still, as fires might be 
supposed to exist in the moon from different causes, 
we should require some marks peculiar to volcanic fires, 
to assure us that such was their origin in a given case. 
Dr. Herschel examined this point with great attention, 
and with better means of observation than any of his 
predecessors enjoyed, and fully embraced the opinion 
that what he saw were volcanoes. In April, 1787, he 
records his observations as follows : "I perceive three 
volcanoes in different places in the dark part of the 
moon. Two of them are already nearly extinct, or oth- 
erwise in a state of going to break out ; the third shows 
an eruption of fire or luminous matter." On the next 
night, he says : " The volcano burns with greater vio- 
lence than last night ; its diameter cannot be less than 
three seconds ; and hence the shining or burning mat- 
ter must be above three miles in diameter. The ap- 
pearance resembles a small piece of burning charcoal, 

* Dick's ' Celestial Scenery,' Chapter IV. 

THE MOON. 167 

when it is covered with a very thin coat of white ashes ; 
and it has a degree of brightness about as strong as that 
with which such a coal would be seen to glow in faint 
daylight." That these were really volcanic fires, he 
considered further evident from the fact, that where a 
fire, supposed to have been volcanic, had been burning, 
there was seen, after its extinction, an accumulation of 
matter, such as would arise from the production of a 
great quantity of lava, sufficient to form a mountain. 

It is probable that the moon has an atmosphere, al- 
though it is difficult to obtain perfectly satisfactory evi- 
dence of its existence ; for granting the existence of an 
atmosphere bearing the same proportion to that planet 
as our atmosphere bears to the earth, its dimensions 
and its density would be so small, that we could detect 
its presence only by the most refined observations. As 
our twilight is owing to the agency of our atmosphere, 
so, could we discern any appearance of twilight in the 
moon, we should regard that fact as indicating that she 
is surrounded by an atmosphere. Or, when the moon 
covers the sun in a solar eclipse, could we see around 
her circumference a faint luminous ring, indicating that 
the sunlight shone through an aerial medium, we might 
likewise infer the existence of such a medium. Such 
a faint ring of light has sometimes, as is supposed, 
been observed. Schroeter, a German astronomer, dis- 
tinguished for the acuteness of his vision and his pow- 
ers of observation in general, was very confident of 
having obtained, from different sources, clear evidence 
of a lunar atmosphere. He concluded, that the infe- 
rior or more dense part of the moon's atmosphere is 
not more than fifteen hundred feet high, and that the 
entire height, at least to the limit where it would be too 
rare to produce any of the phenomena which are relied 
on as proofs of its existence, is not more than a mile. 

It has been a question, much agitated among astron- 
omers, whether there is water in the moon. Analogy 
strongly inclines us to reply in the affirmative. But 
the analogy between the earth and the moon, as deriv- 


ed from all the particulars in which we can compare 
the two bodies, is too feeble to warrant such a conclu- 
sion, and we must have recourse to other evidence, be- 
fore we can decide the point. In the first place, then, 
there is no positive evidence in favor of the existence 
of water in the moon. Those extensive level regions, 
before spoken of, and denominated seas in the geogra- 
phy of this planet, have no other signs of being water, 
except that they are level and dark. But both these 
particulars would characterize an earthly plain, like the 
deserts of Arabia and Africa. In the second place, 
were those dark regions composed of water, the termi- 
nator would be entirely smooth where it passed over 
these oceans or seas. It is indeed indented by few in- 
equalities, compared with those which it exhibits where 
it passes over the mountainous regions ; but still, the 
inequalities are too considerable to permit the conclu- 
sion, that these level spots are such perfect levels as 
water would form. They do not appear to be more 
perfect levels than many plain countries on the globe. 
The deep caverns, moreover, seen in those dusky spots 
which were supposed to be seas, are unfavorable to the 
supposition that those regions are covered by water. In 
the third place, the face of the moon, when illuminated 
by the sun and not obscured by the state of our own 
atmosphere, is always serene, and therefore free from 
clouds. Clouds are objects of great extent ; they fre- 
quently intercept light, like solid bodies ; and did they 
exist about the moon, we should certainly see them, 
and should lose sight of certain parts of the lunar disk 
which they covered. But neither position is true ; we 
neither see any clouds about the moon, with our best 
telescopes, nor do we, by the intervention of clouds, 
ever lose sight of any portion of the moon when our 
own atmosphere is clear. But the want of clouds in the 
lunar atmosphere almost necessarily implies the absence 
of water in the moon. This planet is at the same dis- 
tance from the sun as our own, and has, in this respect, 
on equal opportunity to feel the influence of his rays. 

THE MOON. 169 

Its days are also twenty-seven times as long as ours, 
a circumstance which would augment the solar heat. 
When the pressure of the atmosphere is diminished on 
the surface of water, its tendency to pass into the state 
of vapor is increased. Were the whole pressure of the 
atmosphere removed from the surface of a lake, in a 
Summer's day, when the temperature was no higher 
than seventy-two degrees, the water would begin to 
boil. Now it is well ascertained, that if there be any 
atmosphere about the moon, it is much lighter than 
ours, and presses on the surface of that body with a 
proportionally small force. This circumstance, there- 
fore, would conspire with the other causes mentioned, 
to convert all the water of the moon into vapor, if we 
could suppose it to have existed at any given time. 

But those, who are anxious to furnish the moon and 
other planets with all the accommodations which they 
find in our own, have a subterfuge in readiness, to 
which they invariably resort in all cases like the fore- 
going. " There may be," say they, " some means, un- 
known to us, provided for retaining water on the sur- 
face of the moon, and for preventing its being wast- 
ed by evaporation : perhaps it remains unaltered in 
quantity, imparting to the lunar regions perpetual ver- 
dure and fertility." To this I reply, that the bare pos- 
sibility of a thing is but slight evidence of its reality ; 
nor is such a condition possible, except by miracle. If 
they grant that the laws of Nature are the same in the 
moon as in the earth, then, according to the foregoing 
reasoning, there cannot be water in the moon ; but if 
they say that the laws of Nature are not the same there 
as here, then we cannot reason at all respecting them. 
One who resorts to a subterfuge of this kind ruins his 
own cause. He argues the existence of water in the 
moon, from the analogy of that planet to this. But if 
the laws of Nature are not the same there as here, what 
becomes of his analogy? A liquid substance which 
would not evaporate by such a degree of solar heat as 
falls on the moon, which would not evaporate the faster, 

15 L. A. 4 


in consequence of the diminished atmospheric pressure 
which prevails there, could not be water, for it would 
not have the properties of water, and things are known 
by their properties. Whenever we desert the cardinal 
principle of the Newtonian philosophy, that the laws 
of Nature are uniform throughout all her realms, we 
wander in a labyrinth ; all analogies are made void ; 
all physical reasonings cease ; and imaginary possibili- 
ties or direct miracles take the place of legitimate nat- 
ural causes. 

On the supposition that the moon is inhabited, the 
question has often been raised, whether we may hope 
that our telescopes will ever be so much improved, and 
our other means of observation so much augmented, 
that we shall be able to discover either the lunar inhab- 
itants or any of their works. 

The improbability of our ever identifying artificial 
structures in the moon may be inferred from the fact, 
that a space a mile in diameter is the least space that 
could be distinctly seen. Extensive works of art, as 
large cities, or the clearing up of large tracts of country 
for settlement or tillage, might indeed afford some vari- 
eties of surface ; but they would be merely varieties of 
light and shade, and the individual objects that occa- 
sioned them would probably never be recognised by 
their distinctive characters. Thus, a building equal to 
the great pyramid of Egypt, which covers a space less 
than the fifth of a mile in diameter, would not be dis- 
tinguished by its figure ; indeed, it would be a mere 
point. Still less is it probable that we shall ever dis- 
cover any inhabitants in the moon. Were we to view 
the moon with a telescope that magnifies ten thousand 
times, it would bring the moon apparently ten thous- 
and times nearer, and present it to the eye like a body 
twenty-four miles off. But even this is a distance too 
great for us see the works of man with distinctness. 
Moreover, from the nature of the telescope itself, we 
can never hope to apply a magnifying power so high 
as that here supposed. As I explained to you, when 

THE MOON. 171 

speaking of the telescope, whenever we increase the 
magnifying power of this instrument we diminish its 
field of view, so that with very high magnifiers we can 
see nothing but a point, such as a fixed star. We at 
the same time, also, magnify the vapors and smoke of 
the atmosphere, and all the imperfections of the me- 
dium, which greatly obscures the object, and prevents 
our seeing it distinctly. Hence it is generally most 
satisfactory to view the moon with low powers, which 
afford a large field of view and give a clear light. 
With Clark's telescope, belonging to Yale College, we 
seldom gain any thing by applying to the moon a high- 
er power than one hundred and eighty, although the 
instrument admits of magnifiers as high as four hundred 
and fifty. 

Some writers, however, suppose that possibly we may 
trace indications of lunar inhabitants in their works, and 
that they may in like manner recognise the existence 
of the inhabitants of our planet. An author, who has 
reflected much on subjects of this kind, reasons as fol- 
lows : "A navigator who approaches within a certain 
distance of a small island, although he perceives no 
human being upon it, can judge with certainty that it 
is inhabited, if he perceives human habitations, villages, 
corn-fields, or other traces of cultivation. In like man- 
ner, if we could perceive changes or operations in the 
moon, which could be traced to the agency of intelli- 
gent beings, we should then obtain satisfactory evi- 
dence that such beings exist on that planet ; and it is 
thought possible that such operations may be traced. 
A telescope which magnifies twelve hundred times will 
enable us to perceive, as a visible point on the surface 
of the moon, an object whose diameter is only about 
three hundred feet. Such an object is not larger than 
many of our public edifices ; and therefore, were any 
such edifices rearing in the moon, or were a town or 
city extending its boundaries, or were operations of this 
description carrying on, in a district where no such 
edifices had previously been erected, such objects and 


operations might probably be detected by a minute in- 
spection. Were a multitude of living creatures moving 
from place to place, in a body, or were they even en- 
camping in an extensive plain, like a large army, or 
like a tribe of Arabs in the desert, and afterwards re- 
moving, it is possible such changes might be traced by 
the difference of shade or color, which such movements 
would produce. In order to detect such minute objects 
and operations, it would be requisite that the surface of 
the moon should be distributed among at least a hundred 
astronomers, each having a spot or two allotted to him, 
as the object of his more particular investigation, and 
that the observations be continued for a period of at 
least thirty or forty years, during which time certain 
changes would probably be perceived, arising either 
from physical causes, or from the operations of living 



First to the neighboring Moon this mighty key 
ilied. Behold ! it turned 

The secret wards, it opened wide the course 

And various aspects of the queen of night : 

Whether she wanes into a scanty orb, 

Or, waxing broad, with her pale shadowy light, 

In a soft deluge overflows the sky." Thomson's Elegy. 

LET us now inquire into the revolutions of the moon 
around the earth, and the various changes she under- 
goes every month, called her phases, which depend on 
the different positions she assumes, with respect to the 
earth and the sun, in the course of her revolution. 

The moon revolves about the earth from west to east. 
Her apparent orbit, as traced out on the face of the 
sky, is a great circle ; but this fact would not certainly 
prove that the orbit is really a circle, since, if it were 
an ellipse, or even a more irregular curve, the projec- 

* Dick's ' Celestial Scenery.' 

THE MOON. 173 

tion of it on the face of the sky would be a circle, as 
explained to you before. (See page 148.) The moon 
is comparatively so near to the earth, that her apparent 
movements are very rapid, so that, by attentively watch- 
ing her progress in a clear night, we may see her move 
from star to star, changing her place perceptibly, every 
few hours. The interval during which she goes through 
the entire circuit of the heavens, from any star until 
she comes round to the same star again, is called a si- 
dereal month, and consists of about twenty-seven and 
one fourth days. The time which intervenes between 
one new moon and another is called a synodical month, 
and consists of nearly twenty-nine and a half days. A 
new moon occurs when the sun and moon meet in the 
same part of the heavens ; but the sun as well as the 
moon is apparently travelling eastward, and nearly at 
the rate of one degree a day, and consequently, during 
the twenty-seven days while the moon has been going 
round the earth, the sun has been going forward about 
the same number of degrees in the same direction. 
Hence, when the moon comes round to the part of the 
heavens where she passed the sun last, she does not 
find him there, but must go on more than two days, 
before she comes up with him again. 

The moon does not pursue precisely the same track 
around the earth as the sun does, in his apparent, annual 
motion, though she never deviates far from that track. 
The inclination of her orbit to the ecliptic is only about 
five degrees, and of course the moon is never seen fur- 
ther from the ecliptic than about that distance, and she 
is commonly much nearer to the ecliptic than five de- 
grees. We may therefore see nearly what is the situa- 
tion of the ecliptic in our evening sky at any particu- 
lar time of year, just by watching the path which the 
moon pursues, from night to night, from new to full 

The two points where the moon's orbit crosses the 
ecliptic are called her nodes. They are the intersections 
of the lunar and solar orbits, as the equinoxes are the 


intersections of the equinoctial and ecliptic, and, like the 
latter, are one hundred and eighty degrees apart. 

The changes of the moon, commonly called her 
phases, arise from different portions of her illuminated 
side being turned towards the earth at different times. 
When the moon is first seen after the setting sun, her 
form is that of a bright crescent, on the side of the 
disk next to the sun, while the other portions of the 
disk shine with a feeble light, reflected to the moon 
from the earth. Every night, we observe the moon to 
be further and further eastward of the sun, until, when 
she has reached an elongation from the sun of ninety de- 
grees, half her visible disk is enlightened, and she is 
said to be in her first quarter. The terminator, or 
line which separates the illuminated from the dark 
part of the moon, is convex towards the sun from the 
new to the first quarter, and the moon is said to be 
horned. The extremities of the crescent are called 
cusps. At the first quarter, the terminator becomes a 
straight line, coinciding with the diameter of the disk ; 
but after passing this point, the terminator becomes 
concave towards the sun, bounding that side of the 
moon by an elliptical curve, when the moon is said to 
be gibbous. When the moon arrives at the distance 
of one hundred and eighty degrees from the sun, the 
entire circle is illuminated, and the moon is full. She 
is then in opposition to the sun, rising about the time 
the sun sets. For a week after the full, the moon ap- 
pears gibbous again, until, having arrived within ninety 
degrees of the sun, she resumes the same form as at the 
first quarter, being then at her third quarter. From 
this time until new moon, she exhibits again the form 
of a crescent before the rising sun, until, approaching 
her conjunction with the sun, her narrow thread of 
light is lost in the solar blaze ; and finally, at the mo- 
ment of passing the sun, the dark side is wholly turned 
towards us, and for some time we lose sight of the 

By inspecting Fig, 38, (where T represents the earth, 

Fig. 38. 


A, B, C, &c., the moon in her orbit, and a, b, c, &c., 
her phases, as seen in the heavens,) we shall easily see 
how all these changes occur. 

You have doubtless observed, that the moon appears 
much further in the south at one time than at another, 
when of the same age. This is owing to the fact that 
the ecliptic, and of course the moon's path, which is 
always very near it, is differently situated with respect to 
the horizon, at a given time of night, at different sea- 
sons of the year. This you will see at once, by turning 
to an artificial globe, and observing how the ecliptic 
stands with respect to the horizon, at different peri- 


ods of the revolution. Thus, if we place the two equi- 
noctial points in the eastern and western horizon, Libra 
being in the west, it will represent the position of the 
ecliptic at sunset in the month of September, when the 
sun is crossing the equator ; and at that season of the 
year, the moon's path through our evening sky, one 
evening after another, from new to full, will be nearly 
along the same route, crossing the meridian nearly at 
right angles. But if we place the Winter solstice, or 
first degree of Capricorn, in the western horizon, and 
the first degree of Cancer in the eastern, then the po- 
sition of the ecliptic will be very oblique to the meridi- 
an, the Winter solstice being very far in the southwest, 
and the Summer solstice very far in the northeast ; and 
the course of the moon from new to full will be nearly 
along this track. Keeping these things in mind, we 
may easily see why the moon runs sometimes high and 
sometimes low. Recollect, also, that the new moon is 
always in the same part of the heavens with the sun, 
and that the full moon is in the opposite part of the 
heavens from the sun. Now, when the sun is at the 
Winter solstice, it sets far in the southwest, and accord- 
ingly the new moon runs very low ; but the full moon, 
being in the opposite tropic, which rises far in the 
northeast, runs very high, as is known to be the case in 
mid-winter. But now take the position of the ecliptic 
in mid-summer. Then, at sunset, the tropic of Cancer 
is in the northwest, and the tropic of Capricorn in the 
southeast ; consequently, the new moons run high and 
the full moons low. 

It is a natural consequence of this arrangement, to 
render the moon's light the most beneficial to us, by 
giving it to us in greatest abundance, when we have 
least of the sun's light, and giving it to us most spar- 
ingly, when the sun's light is greatest. Thus, during 
the long nights of Winter, the full moon runs high, 
and continues a very long time above the horizon ; 
while in mid-summer, the full moon runs low, and is 
above the horizon for a much shorter period. This ar- 


rangement operates very favorably to the inhabitants of 
the polar regions. At the season when the sun is ab- 
sent, and they have constant night, then the moon, 
during the second and third quarters, embracing the 
season of full moon, is continually above the horizon, 
compensating in no small degree for the absence of the 
sun ; while, during the Summer months, when the sun 
is constantly above the horizon, and the light of the 
moon is not needed, then she is above the horizon dur- 
ing the first and last quarters, when her light is least, 
affording at that time her greatest light to the inhabi- 
tants of the other hemisphere, from whom the sun is 

About the time of the Autumnal equinox, the moon, 
when near her full, rises about sunset a number of 
nights in succession. This occasions a remarkable 
number of brilliant moonlight evenings ; and as this 
is, in England, the period of harvest, the phenomenon 
is called the harvest moon. Its return is celebrated, 
particularly among the peasantry, by festive dances, and 
kept as a festival, called the harvest home, an occasion 
often alluded to by the British poets. Thus Henry 
Kirke White: 

" Moon of harvest, herald mild 
Of plenty, rustic labor's child, 
Hail, O hail ! 1 greet thy beam, 
As soft it trembles o'er the stream, 
And gilds the straw-thatch'd hamlet wide, 
Where innocence and peace reside ; 
'Tis thou that glad'st with joy the rustic throng, 
Promptest the tripping dance, th' exhilarating song." 

To understand the reason of the harvest moon, we 
will, as before, consider the moon's orbit as coinciding 
with the ecliptic, because we may then take the eclip- 
tic, as it is drawn on the artificial globe, to represent 
that orbit. We will also bear in mind, (what has been 
fully illustrated under the last head,) that, since the 
ecliptic cuts the meridian obliquely, while all the cir- 
cles of diurnal revolution cut it perpendicularly, differ- 
ent portions of the ecliptic will cut the horizon at dif- 


ferent angles. Thus, when the equinoxes are in the 
horizon, the ecliptic makes a very small angle with the 
horizon ; whereas, when the solstitial points are in the 
horizon, the same angle is far greater. In the former 
case, a body moving eastward in the ecliptic, and being 
at the eastern horizon at sunset, would descend but a 
little way below the horizon in moving over many de- 
grees of the ecliptic. Now, this is just the case of the 
moon at the time of the harvest home, about the time 
of the Autumnal equinox. The sun being then in Li- 
bra, and the moon, when full, being of course opposite 
to the sun, or in Aries ; and moving eastward, in or 
near the ecliptic, at the rate of about thirteen degrees 
per day, would descend but a small distance below the 
horizon for five or six days in succession ; that is for 
two or three days before, and the same number of days 
after, the full ; and would consequently rise during all 
these evenings nearly at the same time, namely, a little 
before, or a little after, sunset, so as to afford a remark- 
able succession of fine moonlight evenings. 

The moon turns on her axis in the same time in 
which she revolves around the earth. This is known 
by the moon's always keeping nearly the same face to- 
wards us, as is indicated by the telescope, which could 
not happen unless her revolution on her axis kept pace 
with her motion in her orbit. Take an apple, to rep- 
resent the moon ; stick a knittingneedle through it, in 
the direction of the stem, to represent the axis, in which 
case the two eyes of the apple will aptly represent the 
poles. Through the poles cut a line around the apple, 
dividing it into two hemispheres, and mark them, so 
as to be readily distinguished from each other. Now 
place a candle on the table, to represent the earth, and 
holding the apple by the knittingneedle, carry it round 
the candle, and you will see that, unless you make the 
apple turn round on the axis as you carry it about the 
candle, it will present different sides towards the can- 
dle ; and that, in order to make it always present the 
same side, it will be necessary to make it revolve ex- 


actly once on its axis, while it is going round the circle, 
the revolution on its axis always keeping exact pace 
with the motion in its orbit. The same thing will be 
observed, if you walk around a tree, always keeping 
your face towards the tree. If you have your face to- 
wards the tree when you set out, and walk round with- 
out turning, when you have reached the opposite side 
of the tree, your back will be towards it, and you will 
find that, in order to keep your face constantly towards 
the tree, it will be necessary to turn yourself round on 
your heel at the same rate as you go forward. 

Since, however, the motion of the moon on its axis 
is uniform, while the motion in its orbit is unequal, the 
moon does in fact reveal to us a little sometimes of one 
side and sometimes of the other. Thus if, while car- 
rying the apple round the candle, you carry it forward 
a little faster than the rate at which it turns on its 
axis, a portion of the hemisphere usually out of sight is 
brought into view on one side ; or if the apple is moved 
forward slower than it is turned on its axis, a portion 
of the same hemisphere comes into view on the other 
side. These appearances are called the moon's libra- 
tions in longitude. .The moon has also a libration in 
latitude ; so called, because in one part of her revolu- 
tion more of the region around one of the poles comes 
into view, and, in another part of the revolution, more of 
the region around the other pole, which gives the ap- 
pearance of a tilting motion to the moon's axis. This 
is owing to the fact, that the moon's axis is inclined to 
the plane of her orbit. If, in the experiment with the 
apple, you hold the knittingneedle parallel to the can- 
dle, (in which case the axis will be perpendicular to 
the plane of revolution,) the candle will shine upon 
both poles during the whole circuit, and an eye situated 
where the candle is would constantly see both poles ; 
but now incline the needle towards the plane of revo- 
lution, and carry it round, always keeping it parallel to 
itself, and you will observe that the two poles will be 
alternately in and out of sight. 


The moon exhibits another appearance of this kind, 
called her diurnal libration, depending on the daily 
rotation of the spectator. She turns the same face to- 
wards the centre of the earth only, whereas we view 
her from the surface. When she is on the meridian, 
we view her disk nearly as though we viewed it from 
the centre of the earth, and hence, in this situation, 
it is subject to little change ; but when she is near 
the horizon, our circle of vision takes in more of the 
upper limb than would be presented to a spectator at 
the centre of the earth. Hence, from this cause, we see 
a portion of one limb while the moon is rising, which 
is gradually lost sight of, and we see a portion of the 
opposite limb, as the moon declines to the west. You 
will remark that neither of the foregoing changes im- 
plies any actual motion in the moon, but that each 
arises from a change of position in the spectator. Since 
the succession of day and night depends on the revolu- 
tion of a planet on its own axis, and it takes the moon 
twenty-nine and a half days to perform this revolution, 
so that the sun shall go from the meridian of any place 
and return to the same meridian again, of course the 
lunar day occupies this long period. So protracted an 
exposure to the sun's rays, especiallv in the equatorial 
regions of the moon, must occasion n excessive accu- 
mulation of heat ; and so long an aosence of the sun 
must occasion a corresponding degree of cold. A spec- 
$or on the side of the moon which is opposite to us 
>uld never see ^ earth, but one on the side next to 
us would see the earth constantly in his firmament, un- 
dergoing a gradual succession of changes, corresponding 
to those which the moon exhibits to the earth, but in 
the reverse order. Thus, when it is full moon to us, 
the earth, as seen from the moon, is then in conjunction 
the sun, and of course presents her dark side to 

ooon after this, an inhabitant of the moon would 
see a crescent, resembling our new moon, which would 
in like manner increase and go through all the changes, 


from new to full, and from full to new, as we see them 
in the moon. There are, however, in the two cases, 
several striking points of difference. In the first place, 
instead of twenty-nine and a half days, all these 
changes occur in one lunar day and night. During the 
first and last quarters, the changes would occur in the 
day-time ; but during the second and third quarters, 
during the night. By this arrangement, the lunarians 
would enjoy the greatest possible benefit from the light 
afforded by the earth, since in the half of her revolu- 
tion where she appears to them as full, she would be 
present while the sun was absent, and would afford 
her least light while the sun was present. In the sec- 
ond place, the earth would appear thirteen times as 
large to a spectator on the moon as the moon appears 
to us, and would afford nearly the same proportion of 
light, so that their long nights must be continually 
cheered by an extraordinary degree of light derived from 
this source ; and if the full moon is hailed by our poets 
as " refulgent lamp of night,"* with how much more 
reason might a lunarian exult thus, in view of the splen- 
did orb that adorns his nocturnal sky ! In the third 
place, the earth, as viewed from any particular place 
on the moon, would occupy invariably the same part of 
the heavens. F*' while the rotation of the moon on 
her axis from west to east would appear to make th^ 
earth (as the moon does to us) revolve from east to 
west, the corresponding progress of the moon in h '- 

* " As when the moon, refulgent lamp of night, 

O'er heaven's clear azure sheds her sacred light, ,^^f 

When not a breath disturbs the deep serene, 

And not a cloud o'ercasts the solemn scene, 

Around her throne the vivid planets roll, 

And stars unnumbered jrild the 

O'er the dark trees a yellower 

And tip with silver every moi: id ; 

Then shine the vales, : ' rise, 

A flood of glory hursts from all iliu skies ; 

The conscious swains, rejoicing in the sight, 

Eye the blue vault, and bless the useful light." 

Pope's Homer. 
16 L. A. 


orbit would make the earth appear to revolve from west 
to east ; and as these two motions are equal, their unit- 
ed effect would be to keep the moon apparently stationa- 
ry in the sky. Thus, a spectator at E, Fig. 38, page 175, 
in the middle of the disk that is turned towards the earth, 
would have the earth constantly on his meridian, and 
at E, the conjunction of the earth and sun would 
occur at mid-day ; but when the moon arrived at G, 
the same place would be on the margin of the circle 
of illumination, and will have the sun in the horizon ; 
but the earth would still be on his meridian and in 
quadrature. In like manner, a place situated on the 
margin of the circle of illumination, when the moon is 
at E, would have the earth in the horizon ; and the 
same place would always see the earth in the hori- 
zon, except the slight variations that would occur from 
the librations of the moon. In the fourth place, the 
earth would present to a spectator on the moon none 
of that uniformity of aspect which the moon presents 
to us, but would exhibit an appearance exceedingly 
diversified. The comparatively rapid rotation of the 
earth, repeated fifteen times during a lunar night, would 
present, in rapid succession, a view of our seas, oceans, 
continents, and mountains, all diversified by our clouds, 
storms, and volcanoes. 



u Some say the zodiac constellations 
Have long since left their antique stations, 
Above a sign, and prove the same 
In Taurus now, once in the Ram ; 
That in twelve hundred years and odd, 
The sun has left his ancient road, 
And nearer to the earth is come, 
'Bove fifty thousand miles from home." Hudibras. 

WE have thus far contemplated the revolution of the 
moon around the earth as though the earth were at 


rest. But in order to have just ideas respecting the 
moon's motions, we must recollect that the moon like- 
wise revolves along with the earth around the sun. It 
is sometimes said that the earth carries the moon along 
with her, in her annual revolution. This language 
may convey an erroneous idea ; for the moon, as well 
as the earth, revolves around the sun under the in- 
fluence of two forces, which are independent of the 
earth, and would continue her motion around the sun, 
were the earth removed out of the way. Indeed, the 
moon is attracted towards the sun two and one fifth 
times more than towards the earth, and would abandon 
the earth, were not the latter also carried along with 
her by the same forces. So far as the sun acts equally 
on both bodies, the motion with respect to each other 
would not be disturbed. Because the gravity of the 
moon towards the sun is found to be greater, at the 
conjunction, than her gravity towards the earth, some 
have apprehended that, if the doctrine of universal grav- 
itation is true, the moon ought necessarily to abandon 
the earth. In order to understand the reason why it 
does not do thus, we must reflect, that, when a body is 
revolving in its orbit under the influence of the pro- 
jectile force and gravity, whatever diminishes the force 
of gravity, while that of projection remains the same, 
causes the body to approach nearer to the tangent of 
her orbit, and of course to recede from the centre ; and 
whatever increases the amount of gravity, carries the 
body towards the centre. Thus, in Fig. 33, page 152, 
if, with a certain force of projection acting in the direc- 
tion A B, and of attraction, in the direction A C, the 
attraction which caused a body to move in the line 
A D were diminished, it would move nearer to the tan- 
gent, as in A E, or A F. Now, when the moon is in 
conjunction, her gravity towards the earth acts in oppo- 
sition to that towards the sun, (see Fig. 38, page 175,} 
while her velocity remains too great to carry her with 
what force remains, in a circle about the sun, and she 
therefore recedes from the sun, and commences her 


revolution around the earth. On arriving at the oppo- 
sition, the gravity of the earth conspires with that of 
the sun, and the moon's projectile force being less than 
that required to make her revolve in a circular orbit, 
when attracted towards the sun by the sum of these 
forces, she accordingly begins to approach the sun, and 
descends again to the conjunction. 

The attraction of the sun, however, being every where 
greater than that of the earth, the actual path of the 
moon around the sun is every where concave towards 
the latter. Still, the elliptical path of the moon around 
the earth is to be conceived of, in the same way as 
though both bodies were at rest with respect to the sun. 
Thus, while a steam-boat is passing swiftly around an 
island, and a man is walking slowly around a post in 
the cabin, the line which he describes in space between 
the forward motion of the boat and his circular motion 
around the post, may be every where concave towards 
the island, while his path around the post will still be 
the same as though both were at rest. A nail in the 
rim of a coach-wheel will turn around the axis of the 
wheel, when the coach has a forward motion, in the 
same manner as when the coach is at rest, although the 
line actually described by the nail will be the resultant 
of both motions, and very different from either. 

We have hitherto regarded the moon as describing 
a great circle on the face of the sky, such being the 
visible orbit, as seen by projection. But, on a more 
exact investigation, it is found that her orbit is not a 
circle, and that her motions are subject to very numer- 
ous irregularities. These will be best understood in 
connexion with the causes on which they depend. The 
law of universal gravitation has been applied with won- 
derful success to their developement, and its results have 
conspired with those of long-continued observation, to 
furnish the means of ascertaining with great exactness 
the place of the moon in the heavens, at any given in- 
stant of time, past or future, and thus to enable astron- 
omers to determine longitudes, to calculate eclipses. 


and to solve other problems of the highest interest. 
The whole number of irregularities to which the moon 
is subject is not less than sixty, but the greater part 
are so small as to be hardly deserving of attention ; but 
as many -as thirty require to be estimated and allow- 
ed for, before we can ascertain the exact place of the 
moon at any given time. You will be able to under- 
stand something of the cause of these irregularities, if 
you first gain a distinct idea of the mutual actions of the 
sun, the moon, and the earth. The irregularities in the 
moon's motions are due chiefly to the disturbing influ- 
ence of the sun, which operates in two ways ; first, by 
acting unequally on the earth and moon ; and secondly, 
by acting obliquely on the moon, on account of the in- 
clination of her orbit to the ecliptic. If the sun acted 
equally on the earth and moon, and always in parallel 
lines, this action would serve only to restrain them in 
their annual motions around the sun, and would not 
affect their actions on each other, or their motions 
about their common centre of gravity. In that case, if 
they were allowed to fall towards the sun, they would 
fall equally, and their respective situations would not 
be affected by their descending equally towards it. 
But, because the moon is nearer the sun in one half of 
her orbit than the earth is, and in the other half of her 
orbit is at a greater distance than the earth from the 
sun, while the power of gravity is always greater at a 
less distance ; it follows, that in one half of her orbit 
the moon is more attracted than the earth towards the 
sun, and, in the other half, less attracted than the earth. 
To see the effects of this process, let us suppose that the 
projectile motions of the earth and moon were destroy- 
ed, and that they were allowed to fall freely towards 
the sun. (See Fig. 38, page 175.) If the moon was in 
conjunction with the sun, or in that part of her orbit 
which is nearest to him, the moon would be more attract- 
ed than the earth, and fall with greater velocity towards 
the sun ; so that the distance of the moon from the 
earth would be increased by the fall. If the moon was 


in opposition, or in the part of her orbit which is furthest 
from the sun, she would be less attracted than the earth 
by the sun, and would fall with a less velocity, and be 
left behind ; so that the distance of the moon from the 
earth would be increased in this case, also. If the 
moon was in one of the quarters, then the earth and 
the moon being both attracted towards the centre of 
the sun, they would both descend directly towards that 
centre, and, by approaching it, they would necessarily 
at the same time approach each other, and in this case 
their distance from each other would be diminished. 
Now, whenever the action of the sun would increase 
their distance, if they were allowed to fall towards the 
sun, then the sun's action, by endeavoring to separate 
them, diminishes their gravity to each other ; whenever 
the sun's action would diminish the distance, then it in- 
creases their mutual gravitation. Hence, in the con- 
junction and opposition, their gravity towards each oth- 
er is diminished by the action of the sun, while in the 
quadratures it is increased. But it must be remem- 
bered, that it is not the total action of the sun on them 
that disturbs their motions, but only that part of it which 
tends at one time to separate them, and at another 
time to bring them nearer together. The other and 
far greater part has no other effect than to retain them 
in their annual course around the sun. 

The cause of the lunar irregularities was first investi- 
gated by Sir Isaac Newton, in conformity with his doc- 
trine of universal gravitation, and the explanation was 
first published in the c Principia ;' but, as it was given in 
a mathematical dress, there were at that age very few 
persons capable of reading or understanding it. Sev- 
eral eminent individuals, therefore, undertook to give a 
popular explanation of these difficult points. Among 
Newton's contemporaries, the best commentator was 
M'Laurin, a Scottish astronomer, who published a large 
work entitled ' M'Laurin's Account of Sir Isaac New- 
ton's Discoveries.' No writer of his own day, and, in my 
opinion, no later commentator, has equalled M'Laurin, 


in reducing to common apprehension the leading prin- 
ciples of the doctrine of gravitation, and the explana- 
tion it affords of the motions of the heavenly bodies. 
To this writer I am indebted for the preceding easy 
explanation of the irregularities of the moon's motions, 
as well as for several other illustrations of the same sub- 
lime doctrine. 

The figure of the moon's orbit is an ellipse. We have 
before seen, that the earth's orbit around the sun is of 
the same figure ; and we shall hereafter see this to be 
true of all the planetary orbits. The path of the earth, 
however, departs very little from a circle ; that of the 
moon differs materially from a circle, being considera- 
bly longer one way than the other. Were the orbit a 
circle having the earth in the centre, then the radius 
vector, or line drawn from the centre of the moon to 
the centre of the earth, would always be of the same 
length ; but it is found that the length of the radius 
vector is only fifty-six times the radius of the earth when 
the moon is nearest to us, while it is sixty-four times that 
radius when the moon is furthest from us. The point 
in the moon's orbit nearest the earth is called her peri- 
gee ; the point furthest from the earth, her apogee. We 
always know when the moon is at one of these points, 
by her apparent diameter or apparent velocity ; for, 
when at the perigee, her diameter is greater than at any 
time, and her motion most rapid ; and, on the other 
hand, her diameter is least, and her motion slowest, 
when she is at her apogee. 

The moon's nodes constantly shift their positions 
in the ecliptic, from east to west, at the rate of about 
nineteen and a half degrees every year, returning to 
the same points once in eighteen and a half years. In 
order to understand what is meant by this backward 
motion of the nodes, you must have very distinctly in 
mind the meaning of the terms themselves ; and if, at 
any time, you should be at a loss about the signification 
of any word that is used in expressing an astronomical 
proposition. I would advise you to turn back to the pre- 


vious definition of that term, and revive its meaning 
clearly in the mind, before you proceed any further. 
In the present case, you will recollect that the moon's 
nodes are the two points where her orbit cuts the 
plane of the ecliptic. Suppose the great circle of the 
ecliptic marked out on the face of the sky in a distinct 
line, and let us observe, at any given time, the exact 
moment when the moon crosses this line, which we will 
suppose to be close to a certain star ; then, on its next 
return to that part of the heavens, we shall find that u 
crosses the ecliptic sensibly to the westward of that 
star, and so on, further and further to the westward, 
every time it crosses the ecliptic at either node. This 
fact is expressed by saying that the nodes retrograde 
on the ecliptic; since any motion from east to west, 
being contrary to the order of the signs, is called retro- 
grade. The line which joins these two points, or the 
line of the nodes, is also said to have a retrograde mo- 
tion, or to revolve from east to west once in eighteen 
and a half years. 

The line of the apsides of the moon's orbit revolves 
from west to east, through her whole course, in about 
nine years. You will recollect that the apsides of an 
elliptical orbit are the two extremities of the longer axis 
of the ellipse ; corresponding to the perihelion and aphe- 
lion of bodies revolving about the sun, or to the peri- 
gee and apogee of a body revolving about the earth. 
If, in any revolution of the moon, we should accu- 
rately mark the place in the heavens where the moon is 
nearest the earth, (which may be known by the moon's 
apparent diameter being then greatest,) we should find 
that, at the next revolution, it would come to its peri- 
gee a little further eastward than before, and so on, at 
every revolution, until, after nine years, it would come 
to its perigee nearly at the same point as at first. This 
fact is expressed by saying, that the perigee, and of 
course the apogee, revolves, and that the line which 
joins these two points, or the line of the apsides, also 


These are only a few of the irregularities that attend 
the motions of the moon. These and a few others 
were first discovered by actual observation and have 
been long known ; but a far greater number of lunar 
irregularities have been made known by following out 
all the consequences of the law of universal gravitation. 

The moon may be regarded as a body endeavoring 
to make its way around the earth, but as subject to be 
continually impeded, or diverted from its main course, 
' y the action of the sun and of the earth ; sometimes 
acting in concert and sometimes in opposition to each 
other. Now, by exactly estimating the amount of these 
respective forces, and ascertaining their resultant or 
combined effect, in any given case, the direction and 
velocity of the moon's motion may be accurately deter- 
mined. But to do this has required the highest pow- 
ers of the human mind, aided by all the wonderful 
resources of mathematics. Yet, so consistent is truth 
with itself, that, where some minute inequality in the 
moon's motions is developed at the end of a long and 
intricate mathematical process, it invariably happens, 
that, on pointing the telescope to the moon, and watch- 
ing its progress through the skies, we may actually see 
her commit the same irregularities, unless (as is the 
case with many of them) they are too minute to be 
matters of observation, being beyond the powers of our 
vision, even when aided by the best telescopes. But 
the truth of the law of gravitation, and of the results 
it gives, when followed out by a chain of mathematical 
reasoning, is fully confirmed, even in these minutest 
matters, by the fact that the moon's place in the 
heavens, when thus determined, always corresponds, 
with wonderful exactness, to the place which she is ac- 
tually observed to occupy at that time. 

The mind, that was first able to elicit from the opera- 
tions of Nature the law of universal gravitation, and af- 
terwards to apply it to the complete explanation of all 
the irregular wanderings of the moon, must have giv- 
en evidence of intellectual powers far elevated above 


those of the majority of the human race. We need 
not wonder, therefore, that such homage is now paid 
to the genius of Newton, an admiration which has 
been continually increasing, as new discoveries have 
been made by tracing out new consequences of the 
law of universal gravitation. 

The chief object of astronomical tables is to give 
the amount of all the irregularities that attend the mo- 
tions of the heavenly bodies, by estimating the separate 
value of each, under all the different circumstances in 
which a body can be placed. Thus, with respect to 
the moon, before we can determine accurately the dis- 
tance of the moon from the vernal equinox, that is, her 
longitude at any given moment, we must be able to 
make exact allowances for all her irregularities which 
would affect her longitude. These are in all no less 
than sixty, though most of them are so exceedingly 
minute, that it is not common to take into the account 
more than twenty-eight or thirty. The values of these 
are all given in the lunar tables ; and in finding the 
moon's place, at any given time, we proceed as follows : 
We first find what her place would be on the suppo- 
sition that she moves uniformly in a circle. This gives 
her mean place. We next apply the various correc- 
tions for her irregular motions ; that is, we apply the 
equations, subtracting some and adding others, and 
thus we find her true place. 

The astronomical tables have been carried to such an 
astonishing degree of accuracy, that it is said, by the 
highest authority, that an astronomer could now pre- 
dict, for a thousand years to come, the precise moment 
of the passage of any one of the stars over the merid- 
ian wire of the telescope of his transit-instrument, with 
such a degree of accuracy, that the error would not be 
so great as to remove the object through an angular 
space corresponding to the semidiameter of the finest 
wire that could be made ; and a body which, by the 
tables, ought to appear in the transit-instrument in the 
middle of that wire, would in no case be removed to 


its outer edge. The astronomer, the mathematician, 
and the artist, have united their powers to produce this 
great result. The astronomer has collected the data, 
by long-continued and most accurate observations on 
the actual motions of the heavenly bodies, from night 
to night, and from year to year ; the mathematician has 
taken these data, and applied to them the boundless 
resources of geometry and the calculus ; and, finally, 
the instrument-maker has furnished the means, not 
only of verifying these conclusions, but of discovering 
new truths, as the foundation of future reasonings. 

Since the points where the moon crosses the ecliptic, 
or the moon's nodes, constantly shift their positions 
about nineteen and a half degrees to the westward, 
every year, the sun, in his annual progress in the eclip- 
tic, will go from the node round to the same node again 
in less time than a year, since the node goes to meet 
him nineteen and a half degrees to the west of the 
point where they met before. It would have taken 
the sun about nineteen days to have passed over this 
arc ; and consequently, the interval between two suc- 
cessive conjunctions between the sun and the moon's 
node is about nineteen days shorter than the solar year 
of three hundred and sixty-five days ; that is, it is 
about three hundred and forty-six days ; or, more ex- 
actly, it is 346.619851 days. The time from one new 
moon to another is 29.5305887 days. Now, nineteen 
of the former periods are almost exactly equal to two 
hundred and twenty-three of the latter : 

For 346.619851 X 19=6585.78 days=18 y. 10 d. 

And 29.5305887X223=6585.32 " = " " " 

Hence, if the sun and moon were to leave the 
moon's node together, after the sun had been round to 
the same node nineteen times, the moon would have 
made very nearly two hundred and twenty-three con- 
junctions with the sun. If, therefore, she was in con- 
junction with the sun at the beginning of this period, 
she would be in conjunction again at the end of it; 
and all things relating to the sun, the moon, and the 


node, would be restored to the same relative situation 
as before, and the sun and moon would start again, to 
repeat the same phenomena, arising out of these rela- 
tions, as occurred in the preceding period, and in the 
same order. Now, when the sun and moon meet at 
the moon's node, an eclipse of the sun happens ; and 
during the entire period of eighteen and a half years 
eclipses will happen, nearly in the same manner as they 
did at corresponding times in the preceding period. 
Thus, if there was a great eclipse of the sun on the 
fifth year of one of these periods, a similar eclipse 
(usually differing somewhat in magnitude) might be 
expected on the fifth year of the next period. Hence 
this period, consisting of about eighteen years and ten 
days, under the name of the Saros, was used by the 
Chaldeans, and other ancient nations, in predicting 
eclipses. It was probably by this means that Thales, a 
Grecian astronomer who flourished six hundred years 
before the Christian era, predicted an eclipse of the sun. 
Herodotus, the old historian of Greece, relates that the 
day was suddenly changed into night, and that Thales 
of Miletus had foretold that a great eclipse was to hap- 
pen this year. It was therefore, at that age, considered 
as a distinguished feat to predict even the year in which 
an eclipse was to happen. This eclipse is memorable 
in ancient history, from its having terminated the war 
between the Lydians and the Medes, both parties being 
smitten with such indications of the wrath of the gods. 
The Metonic Cycle has sometimes been confounded 
with the Saros, but it is not the same with it, nor was 
the period used, like the Saros, for foretelling eclipses, 
but for ascertaining the age of the moon at any given 
period. It consisted of nineteen tropical years, during 
which time there are exactly two hundred and thirty- 
five new moons ; so that, at the end of this period, the 
new moons will recur at seasons of the year correspon- 
ding exactly to those of the preceding cycle. If, for 
example, a new moon fell at the time of the vernal equi- 
nox, in one cycle, nineteen years afterwards it would 


occur again at the same equinox ; or, if it had happen- 
ed ten days after the equinox, in one cycle, it would 
also happen ten days after the equinox, nineteen years 
afterwards. By registering, therefore, the exact days 
of any cycle at which the new or full moons occurred, 
such a calendar would show on what days these events 
would occur in any other cycle ; and, since the regula- 
tion of games, feasts, and fasts, has been made very ex- 
tensively, both in ancient and modern times, according 
to new or full moons, such a calendar becomes very con- 
venient for finding the day on which the new or full 
moon required takes place. Suppose, for example, it 
were decreed that a festival should be held on the day 
of the first full moon after the Vernal equinox. Then, 
to find on what day that would happen, in any given 
year, we have only to see what year it is of the lunar 
cycle ; for the day will be the same as it was in the 
corresponding year of the calendar which records all 
the full moons of the cycle for each year, and the re- 
spective days on which they happen. 

The Athenians adopted the metonic cycle four hun- 
dred and thirty-three years before the Christian era, 
for the regulation of their calendars, and had it inscribed 
in letters of gold on the walls of the temple of Minerva. 
Hence the term golden number, still found in our al- 
manacs, which denotes the year of the lunar cycle, 
Thus, fourteen was the golden number for 1837, being 
the fourteenth year of the lunar cycle. 

The inequalities of the moon's motions are divided 
into periodical and secular. Periodical inequalities 
are those which are completed in comparatively short 
periods. Secular inequalities are those which are com- 
pleted only in very long periods, such as centuries or 
ages. Hence the corresponding terms periodical equa- 
tions and secular equations. As an example of a sec- 
ular inequality, we may mention the acceleration of the 
moon's mean motion. It is discovered that the moon 
actually revolves around the earth in a less period now 
than she did in ancient times. The difference, howev- 
17 L. A. 


er, is exceedingly small, being only about ten seconds in 
a century. In a lunar eclipse, the moon's longitude dif- 
fers from that of the sun, at the middle of the eclipse, 
by exactly one hundred and eighty degrees ; and 
since the sun's longitude at any given time of the year 
is known, if we can learn the day and hour when an 
eclipse occurred at any period of the world, we of course 
know the longitude of the sun and moon at that pe- 
riod. Now, in the year 721, before the Christian era, 
Ptolemy records a lunar eclipse to have happened, and 
to have been observed by the Chaldeans. The moon's 
longitude, therefore, for that time, is known ; and as 
we know the mean motions of the moon, at present, 
starting from that epoch, and computing, as may easi- 
ly be done, the place which the moon ought to occupy 
at present, at any given time, she is found to be actual- 
ly nearly a degree and a half in advance of that place. 
Moreover, the same conclusion is derived from a com- 
parison of the Chaldean observations with those made 
by an Arabian astronomer of the tenth century. 

This phenomenon at first led astronomers to appre- 
hend that the moon encountered a resisting medium, 
which, by destroying at every revolution a small portion 
of her projectile force, would have the effect to bring 
her nearer and nearer to the earth, and thus to aug- 
ment her velocity. But, in 1786, La Place demonstra- 
ted that this acceleration is one of the legitimate ef- 
fects of the sun's disturbing force, and is so connected 
with changes in the eccentricity of the earth's orbit, 
that the moon will continue to be accelerated while that 
eccentricity diminishes ; but when the eccentricity has 
reached its minimum, or lowest point, (as it will do, 
after many ages,) and begins to increase, then the 
moon's motions will begin to be retarded, and thus her 
mean motions will oscillate for ever about a mean value. 




" As when the sun, new risen, 

Looks through the horizontal misty air, 
Shorn of his beams, or from behind the moon, 
In dim eclipse, disastrous twilight sheds 
On half the nations, and with fear of change 
Perplexes monarchs : darkened so, yet shone, 
Above them all, the Archangel." Milton. 

HAVING now learned various particulars respecting 
the earth, the sun, and the moon, you are prepared to 
understand the explanation of solar and lunar eclipses, 
which have in all ages excited a high degree of interest. 
Indeed, what is more admirable, than that astronomers 
should be able to tell us, years beforehand, the exact 
instant of the commencement and termination of an 
eclipse, and describe all the attendant circumstances 
with the greatest fidelity. You have doubtless, my 
dear friend, participated in this admiration, and felt a 
strong desire to learn how it is that astronomers are able 
to look so far into futurity. I will endeavor, in this Let- 
ter, to explain to you the leading principles of the cal- 
culation of eclipses, with as much plainness as possible. 

An eclipse of the moon happens when the moon, in 
its revolution around the earth, falls into the earth's 
shadow. An eclipse of the sun happens when the 
moon, coming between the earth and the sun, covers 
either a part or the whole of the solar disk. 

The earth and the moon being both opaque, globular 
bodies, exposed to the sun's light, they cast shadows 
opposite to the sun, like any other bodies on which the 
sun shines. Were the sun of the same size with the 
earth and the moon, then the lines drawn touching the 
surface of the sun and the surface of the earth or moon 
(which lines form the boundaries of the shadow) would 
be parallel to each other, and the shadow would be a 
cylinder infinite in length ; and were the sun less than 



the earth or the moon, the shadow would be an increas- 
ing cone, its narrower end resting on the earth ; but as 
the sun is vastly greater than either of these bodies, 
the shadow of each is a cone whose base rests on the 
body itself, and which comes to a point, or vertex, at a 
certain distance behind the body. These several cases 
are represented in the following diagrams, Figs. 39, 
40, 41. 

Figs. 39, 40, 41. 

It is found, by calculation, that the length of the 
moon's shadow, on an average, is just about sufficient 
to reach to the earth ; but the moon is sometimes fur- 
ther fjom the earth than at others, and when she is 
nearer than usual, the shadow reaches considerably be- 
yond the surface of the earth. Also, the moon, as well 
as the earth, is at different distances from the sun at 
different times, and its shadow is longest when it is 
furthest from the sun. Now, when both these circum- 
stances conspire, that is, when the moon is in her peri- 
gee and along with the earth in her aphelion, her shad- 
ow extends nearly fifteen thousand miles beyond the 
centre of the earth, and covers a space on the surface 
one hundred and seventy miles broad. The earth's 
shadow is nearly a million of miles in length, and con- 
sequently more than three and a half times as long as 
the distance of the earth from the moon ; and it is also, 
at the distance of the moon, three times as broad as the 
moon itself. 


An eclipse of the sun can take place only at new 
moon, when the sun and moon meet in the same part 
of the heavens, for then only can the moon come be- 
tween us and the sun ; and an eclipse of the moon can 
occur only when the sun and moon are in opposite parts 
of the heavens, or at full moon ; for then only can the 
moon fall into the shadow of the earth. 

The nature of eclipses will be clearly understood from 
the following representation. The diagram, Fig. 42, ex- 
Fig. 42. 

hibits the relative position of the sun, the earth, and the 
moon, both in a solar and in a lunar eclipse. Here, the 
moon is first represented, while revolving round the 
earth, as passing between the earth and the sun, and 
casting its shadow on the earth. As the moon is here 
supposed to be at her average distance from the earth, 
the shadow but just reaches the earth's surface. Were 
the moon (as is sometimes the case) nearer the earth, 
her shadow would not terminate in a point, as is repre- 
sented in the figure, but at a greater or less distance 
nearer the base of the cone, so as to cover a considera- 
ble space, which, as I have already mentioned, some- 
times extends to one hundred and seventy miles in 
breadth, but is commonly much less than this. On the 
other side of the earth, the moon is represented as 
traversing the earth's shadow, as is the case in a lunar 


eclipse. As the moon is sometimes nearer the earth 
and sometimes further off, it is evident that it will trav- 
erse the shadow at a broader or a narrower part, ac- 
cordingly. The figure, however, represents the moon 
as passing the shadow further from the earth than is 
ever actually the case, since the distance from the earth 
is never so much as one third of the whole length of the 

It is evident from the figure, that if a spectator were 
situated where the moon's shadow strikes the earth, the 
moon would cut off from him the view of the sun, or 
the sun would be totally eclipsed. Or, if he were 
within a certain distance of the shadow on either side, 
the moon would be partly between him and the sun, 
and would intercept from him more or less of the sun's 
light, according as he was nearer to the shadow or fur- 
ther from it. If he were at c or d, he would just see 
the moon entering upon the sun's disk ; if he were 
nearer the shadow than either of these points, he would 
have a portion of this light cut off from his view, and 
more, in proportion as he drew nearer the shadow ; 
and the moment he entered the shadow, he would lose 
sight of the sun. To all places between a or b and the 
shadow, the sun would cast a partial shadow of the 
moon, growing deeper and deeper, as it approached the 
true shadow. This partial shadow is called the moon's 
penumbra. In like manner, as the moon approaches 
the earth's shadow, in a lunar eclipse, as soon as she 
arrives at a, the earth begins to intercept from her a 
portion of the sun's light, or she falls in the earth's 
penumbra. She continues to lose more and more of 
the sun's light, as she draws near to the shadow, and 
hence her disk becomes gradually obscured, until it en- 
ters the shadow, when the sun's light is entirely lost. 

As the sun and earth are both situated in the plane 
of the ecliptic, if the moon also revolved around the 
earth in this plane, we should have a solar eclipse at 
every new moon, and a lunar eclipse at every full 
moon ; for, in the former case, the moon would come 


directly between us and the sun, and in the latter case, 
the earth would come directly between the sun and 
the moon. But the moon is inclined to the ecliptic 
about five degrees, and the centre of the moon may be 
all this distance from the centre of the sun at new moon, 
and the same distance from the centre of the earth's 
shadow at full moon. It is true, the moon extends 
across her path, one half her breadth lying on each side 
of it, and the sun likewise reaches from the ecliptic a 
distance equal to half his breadth. But these luminaries 
together make but little more than a degree, and con- 
sequently, their two semidiameters would occupy only 
about half a degree of the five degrees from one orbit to 
to the other where they are furthest apart. Also, the 
earth's shadow, where the moon crosses it, extends from 
the ecliptic less than three fourths of a degree, so that 
the semidiameter of the moon and of the earth's shad- 
ow would together reach but little way across the space 
that may, in certain cases, separate the two luminaries 
from each other when they are in opposition. Thus, 
suppose we could take hold of the circle in the figure that 
represents the moon's orbit, (Fig. 42, page 197,) and lift 
the moon up five degrees above the plane of the paper, it 
is evident that the moon, as seen from the earth, would 
appear in the heavens five degrees above the sun, and 
of course would cut off none of his light ; and it is also 
plain that the moon, at the full, would pass the shadow 
of the earth five degrees below it, and would suffer no 
eclipse. But in the course of the sun's apparent revo- 
lution round the earth once a year he is successively in 
every part of the ecliptic ; consequently, the conjunc- 
tions and oppositions of the sun and moon may occur 
at any part of the ecliptic, and of course at the two 
points where the moon's orbit crosses the ecliptic, 
that is, at the nodes ; for the sun must necessarily come 
to each of these nodes once a year. If, then, the moon 
overtakes the sun just as she is crossing his path, she 
will hide more or less of his disk from us. Since, also, 
the earth's shadow is always directly opposite to the 


sun, if the sun is at one of the nodes, the shadow must 
extend in the direction of the other node, so as to lie 
directly across the moon's path ; and if the moon over- 
takes it there, she will pass through it, and be eclipsed. 
Thus, in Fig. 43, let B N represent the sun's path, and 

Fig. 43. 

A N, the moon's, N being the place of the node ; 
then it is evident, that if the two luminaries at new 
moon be so far from the node, that the distances be- 
tween their centres is greater than their semidiameters, 
no eclipse can happen ; but if that distance is less than 
this sum, as at E, F, then an eclipse will take place ; 
but if the position be as at C, D, the two bodies vv 7 ill 
just touch one another. If A denotes the earth's shad- 
ow, instead of the sun, the same illustration will apply 
to an eclipse of the moon. 

Since bodies are defined to be in conjunction when 
they are in the same part of the heavens, and to be in 
opposition when they are in opposite parts of the heav- 
ens, it may not appear how the sun and moon can be in 
conjunction, as at A and B, when they are still at some 
distance from each other. But it must be recollected 
that bodies are in conjunction when they have the same 
longitude, in which case they are situated in the same 
great circle perpendicular to the ecliptic, that is, in 
the same secondary to the ecliptic. One of these bod- 
ies may be much further from the ecliptic than the oth- 
er ; still, if the same secondary to the ecliptic passes 


through them both, they will be in conjunction or op- 

In a total eclipse of the moon, its disk is still visible, 
shining with a dull, red light. This light cannot be 
derived directly from the sun, since the view of the sun 
is completely hidden from the moon ; nor by reflection 
from the earth, since the illuminated side of the earth is 
wholly turned from the moon ; but it is owing to refrac- 
tion from the earth's atmosphere, by which a few scat- 
tered rays of the sun are bent round into the earth's 
shadow and conveyed to the moon, sufficient in number 
to afford the feeble light in question. 

It is impossible fully to understand the method of 
calculating eclipses, without a knowledge of trigonom- 
etry ; still it is not difficult to form some general notion 
of the process. It may be readily conceived that, by 
long-continued observations on the sun and moon, the 
laws of their revolution may be so well understood, that 
the exact places which they will occupy in the heavens 
at any future times may be foreseen and laid down in 
tables of the sun and moon's motions; that we may 
thus ascertain, by inspecting the tables, the instant when 
these two bodies will be together in the heavens, or be 
in conjunction, and when they will be one hundred and 
eighty degrees apart, or in opposition. Moreover, since 
the exact place of the moon's node among the stars at 
any particular time is known to astronomers, it cannot 
be difficult to determine when the new or full moon 
occurs in the same part of the heavens as that where 
the node is projected, as seen from the earth. In short, 
as astronomers can easily determine what will be the 
relative position of the sun, the moon, and the moon's 
nodes, for any given time, they can tell when these 
luminaries will meet so near the node as to produce 
an eclipse of the sun, or when they will be in opposi- 
tion so near the node as to produce an eclipse of the 

A little reflection will enable you to form a clear idea 
of the situation of the sun, the moon, and the earth, at 


the time of a solar eclipse. First, suppose the con- 
junction to take place at the node ; that is, imagine the 
moon to come directly between the earth and the sun, 
as she will of course do, if she comes between the earth 
and the sun the moment she is crossing the ecliptic ; for 
then the three bodies will all lie in one and the same 
straight line. But when the moon is in the ecliptic, 
her shadow, or at least the axis, or central line, of the 
shadow, must coincide with the line that joins the cen- 
tres of the sun and earth, arid reach along the plane of 
the ecliptic towards the earth. The moon's shadow, 
at her average distance from the earth, is just about 
long enough to reach the surface of the earth ; but 
when the moon, at the new, is in her apogee, or at her 
greatest distance from the earth, the shadow is not long 
enough to reach the earth. On the contrary, when the 
moon is nearer to us than her average distance, her 
shadow is long enough to reach beyond the earth, ex- 
tending, when the moon is in her perigee, more than 
fourteen thousand miles beyond the centre of the earth. 
Now, as during the eclipse the moon moves nearly in 
the plane of the ecliptic, her shadow which accompa- 
nies her must also move nearly in the same plane, and 
must therefore traverse the earth across its central re- 
gions, along the terrestrial ecliptic, since this is nothing 
more than the intersection of the plane of the celestial 
ecliptic with the earth's surface. The motion of the 
earth, too, on its axis, in the same direction, will carry 
a place along with the shadow, though with a less ve- 
locity by more than one half ; so that the actual veloc- 
ity of the shadow, in respect to places over which it 
passes on the earth, will only equal the difference be- 
tween its own rate and that of the places, as they are 
carried forward in the diurnal revolution. 

We have thus far supposed that the moon comes to 
her conjunction precisely at the node, or at the moment 
when she is crossing the ecliptic. But, secondly, sup- 
pose she is on the north side of the ecliptic at the time 
of conjunction, and moving towards her descending 


node, and that the conjunction takes place as far from 
the node as an eclipse can happen. The shadow will 
not fall in the plane of the ecliptic, but a little north- 
ward of it, so as just to graze the earth near the pole 
of the ecliptic. The nearer the conjunction comes to 
the node, the further the shadow will fall from the polar 
towards the equatorial regions. 

In a solar eclipse, the shadow of the moon travels 
over a portion of the earth, as the shadow of a small 
cloud, seen from an eminence in a clear day, rides along 
over hills and plains. Let us imagine ourselves stand- 
ing on the moon ; then we shall see the earth partially 
eclipsed by the moon's shadow, in the same manner as 
we now see the moon eclipsed by the shadow of the 
earth ; and we might calculate the various circumstan- 
ces of the eclipse, its commencement, duration, and 
quantity, in the same manner as we calculate these 
elements in an eclipse of the moon, as seen from the 
earth. But although the general characters of a solar 
eclipse might be investigated on these principles, so far 
as respects the earth at large, yet, as the appearances of 
the same eclipse of the sun are very different at differ- 
ent places on the earth's surface, it is necessary to calcu- 
late its peculiar aspects for each place separately, a cir- 
cumstance which makes the calculation of a solar eclipse 
much more complicated and tedious than that of an 
eclipse of the moon. The moon, when she enters the 
shadow of the earth, is deprived of the light of the part 
immersed, and the effect upon its appearance is the 
same as though that part were painted black, in which 
case it would be black alike to all places where the 
moon was above the horizon. But it not so with a so- 
lar eclipse. We do not see this by the shadow cast on 
the earth, as we should do, if we stood on the moon, 
but by the interposition of the moon between us and 
the sun ; and the sun may be hidden from one observ- 
er, while he is in full view of another only a few miles 
distant. Thus, a small insulated cloud sailing in a clear 
sky will, for a few moments, hide the sun from us, 


and from a certain space near us, while all the region 
around is illuminated. But although the analogy be- 
tween the motions of the shadow of a small cloud and 
of the moon in a solar eclipse holds good in many par- 
ticulars, yet the velocity of the lunar shadow is far 
greater than that of the cloud, being no less than two 
thousand two hundred and eighty miles per hour. 

The moon's shadow can never cover a space on the 
earth more than one hundred and seventy miles broad, 
and the space actually covered commonly falls much 
short of that. The portion of the earth's surface ever 
covered by the moon's penumbra is about four thous- 
and three hundred and ninety-three miles. 

The apparent diameter of the moon varies material- 
ly at different times, being greatest when the moon is 
nearest to us, and least when she is farthest off; while 
the sun's apparent dimensions remain nearly the same. 
When the moon is at her average distance from the 
earth, she is just about large enough to cover the sun's 
disk ; consequently, if, in a central eclipse of the sun, 
the moon is at her mean distance, she covers the sun 
but for an instant, producing only a momentary eclipse. 
If she is nearer than her average distance, then the 
eclipse may continue total some time, though never more 
than eight minutes, and seldom so long as that ; but if 
she is further off than usual, or towards her apogee, then 
she is not large enough to cover the whole solar disk, 
but we see a ring of the sun encircling the moon, con- 
stituting an annular eclipse, as seen in Fig. 44. Even 
the elevation of the moon above the horizon will some- 
times sensibly affect the dimensions of the eclipse. You 
will recollect that the moon is nearer to us when on 
the meridian than when in the horizon by nearly four 
thousand miles, or by nearly the radius of the earth ; 
and consequently, her apparent diameter is largest when 
on the meridian. The difference is so considerable, 
that the same eclipse will appear total to a spectator 
who views it near his meridian, while, at the same 
moment, it appears annular to one who has the moon 


near his horizon. An annular eclipse may last, at most, 
twelve minutes and twenty-four seconds. 

Eclipses of the sun are more frequent than those of 
the moon. Yet lunar eclipses being visible to every 
part of the terrestrial hemisphere opposite to the sun, 
while those of the sun are visible only to a small por- 
tion of the hemisphere on which the moon's shadow 
falls, it happens that, for any particular place on the 
earth, lunar eclipses are more frequently visible than 
solar. In any year, the number of eclipses of both 
luminaries cannot be less than two nor more than sev- 
en : the most usual number is four, and it is very rare 
to have more than six. A total eclipse of the moon fre- 
quently happens at the next full moon after an eclipse 
of the sun. For since, in a solar eclipse, the sun is at 
or near one of the moon's nodes, that is, is projected 
to the place in the sky where the moon crosses the 
ecliptic, the earth's shadow, which is of course di- 
rectly opposite to the sun, must be at or near the other 
node, and may not have passed too far from the node 
before the moon comes round to the opposition and 

18 L. A. 


overtakes it. In total eclipses of the sun, there has 
sometimes been observed a remarkable radiation of light 
from the margin of the sun, which is thought to be owing 
to the zodiacal light, which is of such dimensions as to 
extend far beyond the solar orb. A striking appear- 
ance of this kind was exhibited in the total eclipse of 
the sun which occurred in June, 1806. 

A total eclipse of the sun is one of the most sublime 
and impressive phenomena of Nature. Among barba- 
rous tribes it is ever contemplated with fear and aston- 
ishment, and as strongly indicative of the displeasure 
of the gods. Two ancient nations, the Lydians and 
Medes, alluded to before, who were engaged in a bloody 
war, about six hundred years before Christ, were smit- 
ten with such awe, on the appearance of a total eclipse 
of the sun, just on the eve of a battle, that they threw 
down their arms, and made peace. When Columbus 
first discovered America, and was in danger of hostility 
from the Natives, he awed them into submission by 
telling them that the sun would be darkened on a cer- 
tain day, in token of the anger of the gods at them, for 
their treatment of him. 

Among cultivated nations, a total eclipse of the sun 
is recognised, from the exactness with which the time 
of occurrence and the various appearances answer to 
the prediction, as affording one of the proudest tri- 
umphs of astronomy. By astronomers themselves, it is 
of course viewed with the highest interest, not only as 
verifying their calculations, but as contributing to estab- 
lish, beyond all doubt, the certainty of those grand laws, 
the truth of which is involved in the result. I had the 
good fortune to witness the total eclipse of the sun of 
June, 1806, which was one of the most remarkable on 
record. To the wondering gaze of childhood it present- 
ed a spectacle that can never be forgotten. A bright and 
beautiful morning inspired universal joy, for the sky was 
entirely cloudless. Every one was busily occupied in 
preparing smoked glass, in readiness for the great sight, 
which was to be first seen about ten o'clock. A thrill 


of mingled wonder and delight struck every mind when, 
at the appointed moment, a little black indentation 
appeared on the limb of the sun. This gradually ex- 
panded, covering more and more of the solar disk, until 
an increasing gloom was spread over the face of Nature ; 
and when the sun was wholly lost, near mid-day, a feel- 
ing of horror pervaded almost every beholder. The 
darkness was wholly unlike that of twilight or night. 
A thick curtain, very different from clouds, hung upon 
the face of the sky, producing a strange and indescrib- 
ably gloomy appearance, which was reflected from all 
things on the earth, in hues equally strange and unnat- 
ural. Some of the planets, and the largest of the fixed 
stars, shone out through the gloom, yet with their usual 
brightness. The temperature of the air rapidly de- 
clined, and so sudden a chill came over the earth, that 
many persons caught severe colds from their exposure. 
Even the animal tribes exhibited tokens of fear and 
agitation. Birds, especially, fluttered and flew swiftly 
about, and domestic fowls went to rest. 

Indeed, the word eclipse is derived from a Greek word, 
(exleiyis, ekleipsis,) which signifies to fail, to faint or 
swoon away ; since the moon, at the period of her great- 
est brightness, falling into the shadow of the earth, was 
imagined by the ancients to sicken and swoon, as if 
she were going to die. By some very ancient nations 
she was supposed, at such times, to be in pain ; and, in 
order to relieve her fancied distress, they lifted torches 
high in the atmosphere, blew horns and trumpets, beat 
upon brazen vessels, and even, after the eclipse was 
over, they offered sacrifices to the moon. The opinion 
also extensively prevailed, that it was in the power of 
witches, by their spells and charms, not only to darken 
the moon, but to bring her down from her orbit, and 
to compel her to shed her baleful influences upon the 
earth. In solar eclipses, also, especially when total, the 
sun was supposed to turn away his face in abhorrence 
of some atrocious crime, that either had been perpetra- 
ted or was about to be perpetrated, and to threaten 


mankind with everlasting night, and the destruction of 
the world. To such superstitions Milton alludes, in the 
passage which I have taken for the motto of this Letter. 
The Chinese, who, from a very high period of an- 
tiquity, have been great observers of eclipses, although 
they did not take much notice of those of the moon, 
regarded eclipses of the sun in general as unfortunate, 
but especially such as occurred on the first day of the 
year. These were thought to forebode the greatest ca- 
lamities to the emperor, who on such occasions did not 
receive the usual compliments of the season. When, 
from the predictions of their astronomers, an eclipse 
of the sun was expected, they made great preparation 
at court for observing it ; and as soon as it commenc- 
ed, a blind man beat a drum, a great concourse assem- 
bled, and the mandarins, or nobility, appeared in state, 



" First in his east, the glorious lamp was seen, 
Regent of day, and all the horizon round 
Invested with bright rays, jocund to run 
His longitude through heaven's high road ; the gray 
Dawn and the Pleiades before him danced, 
Shedding sweet influence." Milton. 

THE ancients studied astronomy chiefly as subsidiary 
to astrology, with the vain hope of thus penetrating the 
veil of futurity, and reading their destinies among the 
stars. The moderns, on the other hand, have in view, 
as the great practical object of this study, the perfecting 
of the art of navigation. When we reflect on the vast 
interests embarked on the ocean, both of property and 
life, and upon the immense benefits that accrue to soci- 
ety from a safe and speedy intercourse between the 
different nations of the earth, we cannot but see that 
whatever tends to enable the mariner to find his way 
on the pathless ocean, and to secure him against its 


multiplied dangers, must confer a signal benefit on so- 

In ancient times, to venture out of sight of land was 
deemed an act of extreme audacity ; and Horace, the 
Roman poet, pronounces him who first ventured to trust 
his frail bark to the stormy ocean, endued with a heart 
of oak, and girt with triple folds of brass. But now, 
the navigator who fully avails himself of all the resour- 
ces of science, and especially of astronomy, may launch 
fearlessly on the deep, and almost bid defiance to rocks 
and tempests. By enabling the navigator to find his 
place on the ocean with almost absolute precision, how- 
ever he may have been driven about by the winds, and 
however long he may have been out of sight of land, 
astronomers must be held as great benefactors to all 
who commit either their lives or their fortunes to the 
the sea. Nor have they secured to the art of naviga- 
tion such benefits without incredible study and toil, in 
watching the motions of the heavenly bodies, in inves- 
tigating the laws by which their movements are gov- 
erned, and in reducing all their discoveries to a form 
easily available to the navigator, so that, by some sim- 
ple observation on one or two of the heavenly bodies, 
with instruments which the astronomer has invented, 
and prepared for his use, and by looking out a few 
numbers in tables which have been compiled for him, 
with immense labor, he may ascertain the exact place 
he occupies on the surface of the globe, thousands of 
miles from land. 

The situation of any place is known by its latitude and 
longitude. As charts of every ocean and sea are fur- 
nished to the sailor, in which are laid down the latitudes 
and longitudes of every point of land, whether on the 
shores of islands or the main, he has, therefore, only to 
ascertain his latitude and longitude at any particular 
place on the ocean, in order to find where he is, with 
respect to the nearest point of land, although this may 
be, and may always have been, entirely out of sight to 



To determine the latitude of a place is comparatively 
an easy matter, whenever we can see either the sun or 
the stars. The distance of the sun from the zenith, 
when on the meridian, on a given day of the year, 
(which distance we may easily take with the sextant,) 
enables us, with the aid of the tables, to find the lati- 
tude of the place ; or, by taking the altitude of the 
north star, we at once obtain the latitude. 

The longitude of a place may be found by any 
method, by which we may ascertain how much its time 
of day differs from that of Greenwich at the same 
moment. A place that lies eastward of another comes 
to the meridian an hour earlier for every fifteen degrees 
of longitude, and of course has the hour of the day so 
much in advance of the other, so that it counts one 
o'clock when the other place counts twelve. On the 
other hand, a place lying westward of another comes 
to the meridian later by one hour for every fifteen de- 
grees, so that it counts only eleven o'clock when the 
other place counts twelve. Keeping these principles 
in view, it is easy to see that a comparison of the dif- 
ference of time between two places at the same mo- 
ment, allowing fifteen degrees for an hour, sixty min- 
utes for every four minutes of time, and sixty seconds 
for every four seconds of time, affords us an accurate 
mode of finding the difference of longitude between 
the two places. This comparison may be made by 
means of a chronometer, or from solar or lunar eclipses, 
or by what is called the lunar method of finding the 

Chronometers are distinguished from clocks, by be- 
ing regulated by means of a balance-wheel instead of a 
pendulum. A watch, therefore, comes under the gen- 
eral definition of a chronometer ; but the name is more 
commonly applied to larger time-pieces, too large to be 
carried about the person, and constructed with the 
greatest possible accuracy, with special reference to 
finding the longitude. Suppose, then, we are furnished 
with a chronometer set to Greenwich time. We arrive 


at New York, for example, and compare it with the 
time there. We find it is five hours in advance of the 
New-York time, indicating five o'clock, P. M., when it 
is noon at New York. Hence we find that the lon- 
gitude of New York is 5X15=75 degrees.* The 
time at New York, or any individual place, can be 
known by observations with the transit-instrument, 
which gives us the precise moment when the sun is 
on the meridian. 

It would not be necessary to resort to Greenwich, 
for the purpose of setting our chronometer to Green- 
wich time, as it might be set at any place whose lon- 
gitude is known, having been previously determined. 
Thus, if we know that the longitude of a certain place 
is exactly sixty degrees east of Greenwich, we have 
only to set our chronometer four hours behind the 
time at that place, and it will be regulated to Green- 
wich time. Hence it is a matter of the greatest im- 
portance to navigation, that the longitude of numerous 
ports, in different parts of the earth, should be accu- 
rately determined, so that when a ship arrives at any 
such port, it may have the means of setting or verify- 
ing its chronometer. 

This method of taking the longitude seems so easy, 
that you will perhaps ask, why it is not sufficient for all 
purposes, and accordingly, why it does not supersede 
the more complicated and laborious methods? why 
every sailor does not provide himself with a chronom- 
eter, instead of finding his longitude at sea by tedious 
and oft-repeated calculations, as he is in the habit of 
doing? I answer, it is only in a few extraordinary 
cases that chronometers have been constructed of such 
accuracy as to afford results as exact as those obtained 
by the other methods, to be described shortly ; and in- 
struments of such perfection are too expensive for gen- 
eral use among sailors. Indeed, the more common 
chronometers cost too much to come within the means 

* The exact longitude of the City Hall, in the city of New York, 
is 4h.56m.33.5s. 


of a great majority of sea-faring men. Moreover, by 
being transported from place to place, chronometers 
are liable to change their rate. By the rate of any 
time-piece is meant its deviation from perfect accuracy. 
Thus, if a clock should gain one second per day, one 
day with another, and we should find it impossible to 
bring it nearer to the truth, we may reckon this as its 
rate, and allow for it in our estimate of the time of any 
particular observation. If the error was not uniform, 
but sometimes greater and sometimes less than one 
second per day, then the amount of such deviation is 
called its " variation from its mean rate." I introduce 
these minute statements, (which are more precise than 
I usually deem necessary,) to show you to what an 
astonishing degree of accuracy chronometers have in 
some instances been brought. They have been carried 
from London to Baffin's Bay, and brought back, after 
a three years' voyage, and found to have varied from 
their mean rate, during the whole time, only a second 
or two, while the extreme variation of several chronom- 
eters, tried at the Royal Observatory at Greenwich, 
never exceeded a second and a half. Could chronom- 
eters always be depended on to such a degree of accu- 
racy as this, we should hardly desire any thing better 
for determining the longitude of different places on the 
earth. A recent determination of the longitude of the 
City Hall in New York, by means of three chronom- 
eters, sent out from London expressly for that purpose, 
did not differ from the longitude as found by a solar 
eclipse (which is one of the best methods) but a sec- 
ond and a quarter. 

Eclipses of the sun and moon furnish the means of 
ascertaining the longitude of a place, because the en- 
trance of the moon irto the earth's shadow in a lunar 
eclipse, and the entrance of the moon upon the disk 
of the sun in a solar eclipse, are severally examples of 
one of those instantaneous occurrences in the heavens, 
which afford the means of comparing the times of 
different places, and of thus determining their differ- 


ences of longitude. Thus, if the commencement of a 
lunar eclipse was seen at one place an hour sooner than 
at another, the two places would be fifteen degrees 
apart, in longitude ; and if the longitude of one of the 
places was known, that of the other would become 
known also. The exact instant of the moon's entering 
into the shadow of the earth, however, cannot be de- 
termined with very great precision, since the moon, in 
passing through the earth's penumbra, loses its light 
gradually, so that the moment when it leaves the pe- 
numbra and enters into the shadow cannot be very ac- 
curately defined. The first contact of the moon with 
the sun's disk, in a solar eclipse, or the moment of leav- 
ing it, that is, the beginning and end of the eclipse, 
are instants that can be determined with much precis- 
ion, and accordingly they are much relied on for an 
accurate determination of the longitude. But, on ac- 
count of the complicated and laborious nature of the 
calculation of the longitude from an eclipse of the sun, 
(since the beginning and end are not seen at different 
places, at the same moment,) this method of finding 
the longitude is not adapted to common use, nor avail- 
able at sea. It is useful, however, for determining the 
longitude of fixed observatories. The lunar method 
of finding the longitude is the most refined and accu- 
rate of all the modes practised at sea. The motion 
of the moon through the heavens is so rapid, that she 
perceptibly alters her distance from any star every min- 
ute ; consequently, the moment when that distance is a 
certain number of degrees and minutes is one of those 
instantaneous events, which may be taken advantage 
of for comparing the times of different places, and thus 
determining their difference of longitude. Now, in a 
work called the ' Nautical Almanac,' printed in Lon- 
don, annually, for the use of navigators, the distance 
of the moon from the sun by day, or from known fixed 
stars by night, for every day and night in the year, is 
calculated beforehand. If, therefore, a sailor wishes 
to ascertain his longitude, he may take with his sextant 


the distance of the moon from one of these stars at 
any time, suppose nine o'clock, at night, and then 
turn to the ' Nautical Almanac,' and see what time 
it was at Greenwich when the distance between the 
moon and that star was the same. Let it be twelve 
o'clock, or three hours in advance of his time : his 
longitude, of course, is forty-five degrees west. 

This method requires more skill and accuracy than 
are possessed by the majority of seafaring men ; but, 
when practised with the requisite degree of skill, its re- 
sults are very satisfactory. Captain Basil Hall, one of 
the most scientific commanders in the British navy, re- 
lates the following incident, to show the excellence of 
this method. He sailed from San Bias, on the west 
coast of Mexico, and, after a voyage of eight thousand 
miles, occupying eighty-nine days, arrived off Rio de 
Janeiro, having, in this interval, passed through the 
Pacific Ocean, rounded Cape Horn, and crossed the 
South Atlantic, without making any land, or even see- 
ing a single sail, with the exception of an American 
whaler off Cape Horn. When within a week's sail of 
Rio, he set seriously about determining, by lunar obser- 
vations, the precise line of the ship's course, and its sit- 
uation at a determinate moment ; and having ascertain- 
ed this within from five to ten miles, ran the rest of the 
way by those more ready and compendious methods, 
known to navigators, which can be safely employed for 
short trips between one known point and another, but 
which cannot be trusted in long voyages, where the 
moon is the only sure guide. They steered towards Rio 
Janeiro for some days after taking the lunars, and, hav- 
ing arrived within fifteen or twenty miles of the coast, 
they hove to, at four in the morning, till the day should 
break, and then bore up, proceeding cautiously, on ac- 
count of a thick fog which enveloped them. As this 
cleared away, they had the satisfaction of seeing the 
great Sugar-Loaf Rock, which stands on one side of 
the harbor's mouth, so nearly right ahead, that they 
had not to alter their course above a point, in order to 


hit the entrance of the harbor. This was the first land 
they had seen for three months, after crossing so many 
seas, and being set backwards arid forwards by innu- 
merable currents and foul winds. The effect on all on 
board was electric ; and the admiration of the sailors 
was unbounded. Indeed, what could be more admira- 
ble than that a man on the deck of a vessel, by meas- 
uring the distance between the moon and a star, with 
a little instrument which he held in his hand, could 
determine his exact place on the earth's surface in the 
midst of a vast ocean, after having traversed it in all 
directions, for three months, crossing his track many 
times, and all the while out of sight of land ? 

The lunar method of finding the longitude could 
never have been susceptible of sufficient accuracy, had 
not the motions of the moon, with all their irregular- 
ities, been studied and investigated by the most labo- 
rious and profound researches. Hence Newton, while 
wrapt in those meditations which, to superficial minds, 
would perhaps have appeared rather curious than use- 
ful, inasmuch as they respected distant bodies of the 
universe which seemed to have little connexion with 
the affairs of this world, was laboring night and day for 
the benefit of the sailor and the merchant. He was 
guiding the vessel of the one, and securing the mer- 
chandise of the other ; and thus he contributed a large 
share to promote the happiness of his fellow-men, not 
only in exalting the powers of the human intellect, but 
also in preserving the lives and fortunes of those en- 
gaged in navigation and commerce. Principles in sci- 
ence are rules in art ; and the philosopher who is en- 
gaged in the investigation of these principles, although 
his pursuits may be thought less practically useful than 
those of the artisan who carries out those principles 
into real life, yet, without the knowledge of the prin- 
ciples, the rules would have never been known. Stud- 
ies, therefore, the most abstruse, are, when viewed as 
furnishing rules to act, often productive of the highest 
practical utility. 


Since the tides are occasioned by the influence of 
the sun and moon, I will conclude this Letter with a 
few remarks on this curious phenomenon. By the tides 
are meant the alternate rising and falling of the waters 
of the ocean. Its greatest and least elevations are 
called high and low water ; its rising and falling are 
called flood and ebb ; and the extraordinary high and 
low tides that occur twice every month are called spring 
and neap tides. It is high or low tide on opposite 
sides of the globe at the same time. If, for example, 
we have high water at noon, it is also high water to 
those who live on the meridian below us, where it is 
midnight. In like manner, low water occurs simultane- 
ously on opposite sides of the meridian. The average 
amount of the tides for the whole globe is about two and 
a half feet ; but their actual height at different places 
is very various, sometimes being scarcely perceptible, 
and sometimes rising to sixty or seventy feet. At the 
same place, also, the phenomena of the tides are very 
different at different times. In the Bay of Fundy. 
where the tide rises seventy feet, it comes in a mighty 
wave, seen thirty miles off, and roaring with a loud 
noise. At the mouth of the Severn, in England, the 
flood comes up in one head about ten feet high, bring- 
ing certain destruction to any small craft that has been 
unfortunately left by the ebbing waters on the flats ; 
and as it passes the mouth of the Avon, it sends up 
that small river a vast body of water, rising, at Bristol, 
forty or fifty feet. 

Tides are caused by the unequal attractions of the 
sun and moon upon different parts of the earth. Sup- 
pose the projectile force by which the earth is carried 
forward in her orbit to be suspended, and the earth to 
fall towards one of these bodies, the moon, for exam- 
ple, in consequence of their mutual attraction. Then, 
if all parts of the earth fell equally towards the moon, 
no derangement of its different parts would result, any 
more than of the particles of a drop of water, in its de- 
scent to the ground. But if one part fell faster than 

TIDES. 217 

another, the different portions would evidently be sep- 
arated from each other. Now, this is precisely what 
takes place with respect to the earth, in its fall towards 
the moon. The portions of the earth in the hemis- 
phere next to the moon, on account of being nearer to 
the centre of attraction, fall faster than those in the 
opposite hemisphere, and consequently leave them be- 
hind. The solid earth, on account of its cohesion, can- 
not obey this impulse, since all its different portions 
constitute one mass, which is acted on in the same 
manner as though it were all collected in the centre ; 
but the waters on the surface, moving freely under 
this impulse, endeavor to desert the solid mass and fall 
towards the moon. For a similar reason, the waters in 
the opposite hemisphere, falling less towards the moon 
than the solid earth does, are left behind, or appear to 

But if the moon draws the waters of the earth into 
an oval form towards herself, raising them simultane- 
ously on the opposite sides of the earth, they must ob- 
viously be drawn away from the intermediate parts of 
the earth, where it must at the same time be low water. 

Fig. 46. 

Thus, in Fig. 46, the moon, M, raises the waters be- 
neath itself at Z and N, at which places it is high wa- 
19 L. A. 


ter, but at the same time depresses the waters at H and 
R, at which places it is low water. Hence, the inter- 
val between the high and low tide, on successive days, 
is about fifty minutes, corresponding to the progress of 
the moon in her orbit from west to east, which causes 
her to come to the meridian about fifty minutes later 
every day. There occurs, however, an intermediate 
tide, when the moon is on the lower meridian, so that 
the interval between two high tides is about twelve 
hours, and twenty-five minutes. 

Were it not for the impediments which prevent the 
force from producing its full effects, we might expect 
to see the great tide- wave, as the elevated crest is 
called, always directly beneath the moon, attending it 
regularly around the globe. But the inertia of the 
waters prevents their instantly obeying the moon's at- 
traction, and the friction of the waters on the bottom 
of the ocean still further retards its progress. It is 
not, therefore, until several hours (differing at different 
places) after the moon has passed the meridian of a 
place, that it is high tide at that place. 

The sun has an action similar to that of the moon, 
but only one third as great. On account of the great 
mass of the sun, compared with that of the moon, we 
might suppose that his action in raising the tides would 
be greater than the moon's ; but the nearness of the 
moon to the earth more than compensates for the sun's 
greater quantity of matter. As, however, wrong views 
are frequently entertained on this subject, let us en- 
deavor to form a correct idea of the advantage which 
the moon derives from her proximity. It is not that 
her actual amount of attraction is thus rendered great- 
er than that of the sun ; but it is that her attraction for 
the different parts of the earth is very unequal, while 
that of the sun is nearly uniform. It is the inequality 
of this action, and not the absolute force, that produces 
the tides. The sun being ninety-five millions of miles 
from the earth, while the diameter of the earth is only 
one twelve thousandth part of this distance, the effects 

TIDES. 219 

of the sun's attraction will be nearly the same on all 
parts of the earth, and therefore will not, as was ex- 
plained of the moon, tend to separate the waters from 
the earth on the nearest side, or the earth from the wa- 
ters on the remotest side, but in a degree proportional- 
ly smaller. But the diameter of the earth is one thir- 
tieth the distance of the moon, and therefore the moon 
acts with considerably greater power on one part of the 
earth than on another. 

As the sun and moon both contribute to produce the 
tides, and as they sometimes act together and some- 
times in opposition to each other, so corresponding va- 
riations occur in the height of the tide. The spring 
tides, or those which rise to an unusual height twice a 
month, are produced by the sun and moon's acting to- 
gether ; and the neap tides, or those which are unus- 
ually low twice a month, are produced by the sun and 
moon's acting in opposition to each other. The spring 
tides occur at the syzygies : the neap tides at the quad- 
ratures. At the time of new moon, the sun and moon 
both being on the same side of the earth, and acting 
upon it in the same line, their actions conspire, and the 
sun may be considered as adding so much to the force 
of the moon. We have already seen how the moon 
contributes to raise a tide on the opposite side of the 
earth. But the sun, as well as the moon, raises its own 
tide-wave, which at new moon coincides with the lu- 
nar tide-wave. This will be plain on inspecting the di- 
agram, Fig. 47, on page 220, where S represents the sun, 
C, the moon in conjunction, O, the moon in opposition, 
and Z, N, the tide-wave. Since the sun and moon 
severally raise a tide- wave, and the two here coincide, 
it is evident that a peculiarly high tide must occur 
when the two bodies are in conjunction, or at new 
moon. At full moon, also, the two luminaries conspire 
in the same way to raise the tide ; for we must recol- 
lect that each body contributes to raise a tide on the 
opposite side. Thus, when the sun is at S and the 
moon at O, the sun draws the waters on the side next 


Fig. 47. 

to it away from the earth, and the moon draws the 
earth away from the waters on that side ; their united 
actions, therefore, conspire, and an unusually high tide 
is the result. On the side next to O, the two forces 
likewise conspire : for while the moon draws the wa- 
ters away from the earth, the sun draws the earth away 
from the waters. In both cases an unusually low tide 
is produced ; for the more the water is elevated at Z 
and N, the more it will be depressed at H and R, the 
places of low tide. 

Twice a month, also, namely, at the quadratures of 
the moon, the tides neither rise so high nor fall so low 
as at other times, because then the sun and moon act 
against each other. Thus, in Fig. 48, while F tends 
to raise the water at Z, S tends to depress it, and 
consequently the high tide is less than usual. Again, 
while F tends to depress the water at R, S tends to 
elevate it. and therefore the low tide is less than usual. 
Hence the difference between high and low water is 
only half as great at neap as at spring tide. In the 
diagrams, the elevation and depression of the waters is 
represented, for the sake of illustration, as far greater 

TIDES. 221 

Fig. 48. 

than it really is ; for you must recollect that the aver- 
age height of the tides for the whole globe is only 
about two and a half feet, a quantity so small, in com- 
parison with the diameter of the earth, that were the 
due proportions preserved in the figures, the effect 
would be wholly insensible. 

The variations of distance in the sun are not great 
enough to influence the tides very materially, but the 
variations in the moon's distances have a striking effect. 
The tides which happen, when the moon is in perigee, 
are considerably greater than when she is in apogee ; 
and if she happens to be in perigee at the time of the 
syzygies, the spring tides are unusually high. 

The motion of the tide-wave is not a progressive mo- 
tion, but a mere undulation, and is to be carefully dis- 
tinguished from the currents to which it gives rise. If 
the ocean completely covered the earth, the sun and 
moon being in the equator, the tide-wave would travel 
at the same rate as the earth revolves on its axis. In- 
deed, the correct way of conceiving of the tide-wave, 
is to consider the moon at rest, and the earth, in its ro- 
tation from west to east, as bringing successive portions 


of water under the moon, which portions being eleva- 
ted successively, at the same rate as the earth revolves 
on its axis, have a relative motion westward, at the 
same rate. 

The tides of rivers, narrow bays, and shores far from 
the main body of the ocean, are not produced in those 
places by the direct action of the sun and moon, but 
are subordinate waves propagated from the great tide- 
wave, and are called derivative tides, while those raised 
directly by the sun and moon are called primitive 

The velocity with which the tide moves will depend 
on various circumstances, but principally on the depth, 
and probably on the regularity, of the channel. If the 
depth is nearly uniform the tides will be regular ; but 
if some parts of the channel are deep while others are 
shallow, the waters will be detained by the greater fric- 
tion of the shallow places, and the tides will be irregu- 
lar. The direction, also, of the derivative tide may be 
totally different from that of the primitive. Thus, in 
Fig. 49, if the great tide-wave, moving from east to 

Fig. 49. 

west, is represented by the lines 1, 2, 3, 4, the deriva- 
tive tide, which is propagated up a river or bay, will 

TIDES. 223 

be represented by the lines 3, 4, 5, 6, 7. Advancing 
faster in the channel than next the bank, the tides will 
lag behind towards the shores, and the tide-wave will 
take the form of curves, as represented in the diagram. 

On account of the retarding influence of shoals, and 
an uneven, indented coast, the tide-wave travels more 
slowly along the shores of an island than in the neigh- 
boring sea, assuming convex figures at a little distance 
from the island, and on opposite sides of it. These con- 
vex lines sometimes meet, and become blended in such 
a way, as to create singular anomalies in a sea much 
broken by islands, as well as on coasts indented with 
numerous bays and rivers. Peculiar phenomena are 
also produced, when the tide flows in at opposite ex- 
tremities of a reef or island, as into the two opposite 
ends of Long-Island Sound. In certain cases, a tide- 
wave is forced into a narrow arm of the sea, and pro- 
duces very remarkable tides. The tides of the Bay of 
Fundy (the highest in the world) are ascribed to this 
cause. The tides on the coast of North America are 
derived from the great tide-wave of the South Atlantic, 
which runs steadily northward along the coast to the 
mouth of the Bay of Fundy, where it meets the north- 
ern tide-wave flowing in the opposite direction. This 
accumulated wave being forced into the narrow space 
occupied by the Bay, produces the remarkable tide of 
that place. 

The largest lakes and inland seas have no percepti- 
ble tides. This is asserted by all writers respecting 
the Caspian and Euxine ; and the same is found to be 
true of the largest of the North- American lakes, Lake 
Superior. Although these several tracts of water ap- 
pear large, when taken by themselves, yet they occupy 
but small portions of the surface of the globe, as will 
appear evident from the delineation of them on the 
artificial globe. Now, we must recollect that the prim- 
itive tides are produced by the unequal action of the 
sun and moon upon the different parts of the earth ; 
and that it is only at points whose distance from each 


other bears a considerable ratio to the whole distance 
of the sun or moon, that the inequality of action be- 
comes manifest. The space required to make the ef- 
fect sensible is larger than either of these tracts of wa- 
ter. It is obvious, also, that they have no opportunity 
to be subject to a derivative tide. 

Although all must admit that the tides have some 
connexion with the sun and the moon, yet there are so 
many seeming anomalies, which at first appear irrecon- 
cilable with the theory of gravitation, that some are un- 
willing to admit the explanation given by this theory. 
Thus, the height of the tide is so various, that at some 
places on the earth there is scarcely any tide at all, 
while at other places it rises to seventy feet. The time 
of occurrence is also at many places wholly unconform- 
able to the motions of the moon, as is required by the 
theory, being low water where it should be high water ; 
or, instead of appearing just beneath the moon, as the 
theory would lead us to expect, following it at the dis- 
tance of six, ten, or even fifteen, hours ; and finally, the 
moon sometimes appears to have no part at all in pro- 
ducing the tide, but it happens uniformly at noon and 
midnight, (as is said to be the case at the Society Isl- 
ands,) and therefore seems wholly dependent on the sun. 

Notwithstanding these seeming inconsistencies with 
the law of universal gravitation, to which the explana- 
tion of the tides is referred, the correspondence of the 
tides to the motions of the sun and moon, in obedience 
to the law of attraction, is in general such as to warrant 
the application of that law to them, while in a great 
majority of the cases which appear to be exceptions to 
the operation of that law, local causes and impediments 
have been discovered, which modified or overruled the 
uniform operation of the law of gravitation. Thus it 
does not disprove the reality of the existence of a force 
which carries bodies near the surface of the earth tow- 
ards its centre, that we see them sometimes compelled, 
by the operation of local causes, to move in the oppo- 
site direction. A ball shot from a cannon is still subject 


to the law of gravitation, although, for a certain time, in 
obedience to the impulse given it, it may proceed in a 
line contrary to that in which gravity alone would car- 
ry it. The fact that water may be made to run up hill 
does not disprove the fact that it usually runs down 
hill by the force of gravity, or that it is still subject to 
this force, although, from the action of modifying or 
superior forces, it may be proceeding in a direction con- 
trary to that given by gravity. Indeed, those who have 
studied the doctrine of the tides most profoundly con- 
sider them as affording a striking and palpable exhibi- 
tion of the truth of the doctrine of universal gravitation. 



" First, Mercury, amidst full tides of light, 
Rolls next the sun, through his small circle bright; 
Our earth would blaze beneath so fierce a ray, 
And all its marble mountains melt away. 
Fair Venus next fulfils her larger round, 
With softer beams, and milder glory crowned ; 
Friend to mankind, she glitters from afar, 
Now the bright evening, now the morning, star." Baker. 

THERE is no study in which more is to be hoped for 
from a lucid arrangement, than in the study of astrono- 
my. Some subjects involved in this study appear very 
difficult and perplexing to the learner, before he has 
fully learned the doctrine of the sphere, and gained a 
certain familiarity with astronomical doctrines, which 
would seem very easy to him after he had made such 
attainments. Such an order ought to be observed, as 
shall bring out the facts and doctrines of the science 
just in the place where the mind of the learner is pre- 
pared to receive them. Some writers on astronomy 
introduce their readers at once to the most perplexing 
part of the whole subject, the planetary motions. I 
have thought a different course advisable, and have 
therefore commenced these Letters with an account of 


those bodies which are most familiarly known to us, the 
earth, the sun, and the moon. In connexion with the 
earth, we are able to acquire a good knowledge of the 
artificial divisions and points of reference that are es- 
tablished on the earth and in the heavens, constituting 
the doctrine of the sphere. You thus became familiar 
with many terms and definitions which are used in as- 
tronomy. These ought to be always very clearly borne 
in mind ; and if you now meet with any term, the defi- 
nition of which you have either partially or wholly for- 
gotten, let me strongly recommend to you, to turn back 
and review it, until it becomes as familiar to you as 
household words. Indeed, you will find it much to 
your advantage to go back frequently, and reiterate 
the earlier parts of the subject, before you advance to 
subjects of a more intricate nature. If this process 
should appear to you a little tedious, still you will find 
yourself fully compensated by the clear light in which 
all the succeeding subjects will appear. This clear and 
distinct perception of the ground we have been over 
shows us just where we are on our journey, and helps us 
to find the remainder of the way with far greater ease 
than we could otherwise do. I do not, however, pro- 
pose by any devices to relieve you from the trouble 
of thinking. Those who are not willing to incur this 
trouble can never learn much of astronomy. 

In introducing you to the planets, (which next claim 
our attention,) I will, in the first place, endeavor to 
convey to you some clear views of these bodies indi- 
vidually, and afterwards help you to form as correct a 
notion as possible of their motions and mutual relations. 

The name planet is derived from a Greek word, 
(7tlavrjirjz,planetes,} which signifies a wanderer, and is 
applied to this class of bodies, because they shift their 
positions in the heavens, whereas the fixed stars con- 
stantly maintain the same places with respect to each 
other. The planets known from a high antiquity are, 
Mercury, Venus, Earth, Mars, Jupiter, and Saturn. To 
these, in 1781, was added Uranus, (or Herschel, as it 


is sometimes called, from the name of its discoverer ;) 
and, as late as the commencement of the present cen- 
tury, four more were added, namely, Ceres, Pallas, Ju- 
no, and Vesta. These bodies are designated by the 
following characters : 

1. Mercury, 7. Ceres, ^ 

2. Venus, 9 8. Pallas, $ 

3. Earth, 9. Jupiter, ^ 

4. Mars, ^ 10. Saturn, \ 

5. Vesta, jj 11. Uranus, $ 

6. Juno, 5 

The foregoing are called the primary planets. Sev- 
eral of these have one or more attendants, or satellites, 
which revolve around them as they revolve around the 
sun. The Earth has one satellite, namely, the Moon ; 
Jupiter has four ; Saturn, seven ; and Uranus, six. 
These bodies are also planets, but, in distinction from 
the others, they are called secondary planets. Hence, 
the whole number of planets are twenty-nine, namely, 
eleven primary, and eighteen secondary, planets. 

You need never look for a planet either very far in 
the north or very far in the south, since they are al- 
ways near the ecliptic. Mercury, which deviates fur- 
thest from that great circle, never is seen more than 
seven degrees from it ; and you will hardly ever see 
one of the planets so far from it as this, but they all 
pursue nearly the same great route through the skies, 
in their revolutions around the sun. The new planets, 
however, make wider excursions from the plane of the 
ecliptic, amounting, in the case of Pallas, to thirty-four 
and a half degrees. 

Mercury and Venus are called inferior planets, be- 
cause they have their orbits nearer to the sun than that 
of the earth ; while all the others, being more distant 
from the sun than the earth, are called superior plan- 
ets. The planets present great diversities among them- 
selves, in respect to distance from the sun, magnitude, 
time of revolution, and density. They differ, also, in 


regard to satellites, of which, as we have seen, three 
have respectively four, six, and seven, while more than 
half have none at all. It will aid the memory, and ren- 
der our view of the planetary system more clear and com- 
prehensive, if we classify, as far as possible, the various 
particulars comprehended under the foregoing heads. 
As you have had an opportunity, in preceding Let- 
ters, of learning something respecting the means which 
astronomers have of ascertaining the distances and mag- 
nitudes of these bodies, you will not doubt that they 
are really as great as they are represented ; but when 
you attempt to conceive of spaces so vast, you will find 
the mind wholly inadequate to the task. It is indeed 
but a comparatively small space that we can fully com- 
prehend at one grasp. Still, by continual and repeat- 
ed efforts, we may, from time to time, somewhat enlarge 
the boundaries of our mental vision. Let us begin 
with some known and familiar space, as the distance 
between two places we are accustomed to traverse. 
Suppose this to be one hundred miles. Taking this as 
our measure, let us apply it to some greater distance, 
as that across the Atlantic Ocean, say three thousand 
miles. From this step we may advance to some faint 
conception of the diameter of the earth ; and taking 
that as a new measure, we may apply it to such greater 
spaces as the distance of the planets from the sun. I 
hope you will make trial of this method on the follow- 
ing comparative statements respecting the planets. 

Distances from the Sun, in miles. 

I. Mercury, 37,000,000 6. Juno, ) 

-2. Venus, 68,000,000 7. Ceres, V 261,000,000 

3. Earth, 95,000,000 8. Pallas, ) 

4. Mars, 142,000,000 9. Jupiter, 485,000,000 

5. Vesta, 225,000,000 10. Saturn, 890,000,000 

11. Uranus, or Herschel, 1800,000,000 

The dimensions of the planetary system are seen 
from this table to be vast, comprehending a circular 


space thirty-six hundred millions of miles in diameter. 
A rail-way car, travelling constantly at the rate of twen- 
ty miles an hour, would require more than twenty 
thousand years to cross the orbit of Uranus. 


Diam. in miles. Diam. in miles. 

1. Mercury, 3140 5. Ceres, 160 

2. Venus, 7700 6. Jupiter, 89,000 

3. Earth, 7912 7. Saturn, 79,000 

4. Mars, 4200 8. Uranus, 35,000 
We remark here a great diversity in regard to mag- 
nitude, a diversity which does not appear to be sub- 
ject to any definite law. While Venus, an inferior 
planet, is nine tenths as large as the earth, Mars, a 
superior planet, is only one seventh, while Jupiter is 
twelve hundred and eighty-one times as large. Al- 
though several of the planets, when nearest to us, 
appear brilliant and large, when compared with most 
of the fixed stars, yet the angle which they subtend is 
very small, that of Venus, the greatest of all, never 
exceeding about one minute, which is less than one 
thirtieth the apparent diameter of the sun or moon, 
Jupiter, also, by his superior brightness, sometimes 
makes a striking figure among the stars ; yet his great- 
est apparent diameter is less than one fortieth that of 
the sun. 

Periodic Times. 

Mercury revolves around the sun in nearly 3 months. 
Venus, " " " " 7J " 

Earth, " " 1 year. 

Mars, " " 2 years. 

Ceres, " " " " 4| " 

Jupiter, " " " 12 

Saturn, " " " " 29 " 

Uranus, " " " " 84 " 

From this view, it appears that the planets nearest 
the sun move most rapidly. Thus, Mercury performs 

20 L. A. 


nearly three hundred and fifty revolutions while Ura- 
nus performs one. The apparent progress of the most 
distant planets around the sun is exceedingly slow. 
Uranus advances only a little more than four degrees 
in a whole year ; so that we find this planet occupying 
the same sign, and of course remaining nearly in the 
same part of the heavens, for several years in succes- 

After this comparative view of the planets in gener- 
al, let us now look at them individually ; and first, of 
the inferior planets, Mercury and Venus. 

MERCURY and VENUS, having their orbits so far with- 
in that of the earth, appear to us as attendants upon 
the sun. Mercury never appears further from the sun 
than twenty-nine degrees, and seldom so far ; and Ve- 
nus, never more than about forty-seven degrees. Both 
planets, therefore, appear either in the west soon after 
sunset, or in the east a little before sunrise. In high 
latitudes, where the twilight is long, Mercury can sel- 
dom be seen with the naked eye, and then only when 
its angular distance from the sun is greatest. Coper- 
nicus, the great Prussian astronomer, (who first dis- 
tinctly established the order of the solar system, as at 
present received,) lamented, on his death-bed, that he 
had never been able to obtain a sight of Mercury ; 
and Delambre, a distinguished astronomer of France, 
saw it but twice. In our latitude, however, we may 
see this planet for several evenings and mornings, if 
we will watch the time (as usually given in the alma- 
nac) when it is at its greatest elongations from the sun. 
It will not, however, remain long for our gaze, but will 
soon run back to the sun. The reason of this will be 
readily understood from the following diagram, Fig. 
50. Let S represent the sun, E, the earth, and M, N, 
Mercury at its greatest elongations from the sun, and 
O Z P, a portion of the sky. Then, since we refer all 
distant bodies to the same concave sphere of the heav- 
ens, it is evident that we should see the sun at Z, and 
Mercury at O, when at its greatest eastern elongation, 




and at P, when at its greatest western elongation ; and 
while passing from M to N through Q,, it would appear 
to describe the arc O P ; and while passing from N to 
M through R, it would appear to run back across the 
sun on the same arc. It is further evident that it 
would be visible only when at or near one of its great- 
est elongations ; being at all other times so near the 
sun as to be lost in his light. 

A planet is said to be in conjunction with the sun 
when it is seen in the same part of the heavens with the 
sun. Mercury and Venus have each two conjunctions, 
the inferior and the superior conjunction. The infe- 
rior conjunction is its position when in conjunction on 
the same side of the sun with the earth, as at Q,, in the 
figure : the superior conjunction is its position when on 
the side of the sun most distant from the earth, as at R. 

The time which a planet occupies in making one 
entire circuit of the heavens, from any star, until it 
comes round to the same star again, is called its side- 
real revolution. The period occupied by a planet be- 
tween two successive conjunctions with the earth is 
called its synodical revolution. Both the planet and 



the earth being in motion, the time of the sy nodical 
revolution of Mercury or Venus exceeds that of the si- 
dereal ; for when the planet comes round to the place 
where it before overtook the earth, it does not find the 
earth at that point, but far in advance of it. Thus, let 
Mercury come into inferior conjunction with the earth 
at C, Fig. 51. In about eighty-eight days, the planet 
will come round to the same point again ; but, mean- 
while, the earth has moved forward through the arc 
E E', and will continue to move while the planet is 
moving more rapidly to overtake her ; the case being 
analogous to that of the hour and minute hand of a 

Fig. 51. 

The synodical period of Mercury is one hundred and 
sixteen days, and that of Venus five hundred and eigh- 
ty-four days. The former is increased twenty-eight 
days, and the latter, three hundred and sixty days, by 
the motion of the earth ; so that Venus, after being in 
conjunction with the earth, goes more than twice round 
the sun before she comes into conjunction again. For, 
since the earth is likewise in motion, and moves more 


than half as fast as Venus, by the time the latter has 
gone round and returned to the place where the two 
bodies were together, the earth is more than half way 
round, and continues moving, so that it will be a long 
time before Venus comes up with it. 

The motion of an inferior planet is direct in pass- 
ing through its superior conjunction, and retrograde in 
passing through its inferior conjunction. You will 
recollect that the motion of a heavenly body is said to 
be direct when it is in the order of the signs from west 
to east, and retrograde when it is contrary to the order 
of the signs, or from east to west. Now Venus, while 
going from B through D to A, (Fig. 51,) moves from 
west to east, and would appear to traverse the celes- 
tial vault B' S' A', from right to left ; but in passing 
from A through C to B, her course would be retrograde, 
returning on the same arc from left to right. If the 
earth were at rest, therefore, (and the sun, of course, 
at rest,) the inferior planets would appear to oscillate 
backwards and forwards across the sun. But it must 
be recollected that the earth is moving in the same di- 
rection with the planet, as respects the signs, but with 
a slower motion. This modifies the motions of the 
planet, accelerating it in the superior, and retarding 
it in the inferior, conjunction. Thus, in Fig. 51, Ve- 
nus, while moving through B D A, would seem to 
move in the heavens from B' to A', were the earth at 
rest ; but, mean-while, the earth changes its position 
from E to E', on which account the planet is not seen 
at A', but at A", being accelerated by the arc A' A", in 
consequence of the earth's motion. On the other hand, 
when the planet is passing through its inferior conjunc- 
tion A C B, it appears to move backwards in the heavens 
from A' to B', if the earth is at rest, but from A' to B", if 
the earth has in the mean time moved from E to E', 
being retarded by the arc B' B". Although the motions 
of the earth have the effect to accelerate the planet in 
the superior conjunction, and to retard it in the infe- 
rior, yet, on account of the greater distance, the appa- 


rent motion of the planet is much slower in the supe- 
rior than in the inferior conjunction, Venus being the 
whole breadth of her orbit, or one hundred and thirty- 
six millions of miles further from us when at her great- 
est, than when at her least, distance, as is evident from 
Fig. 51. When passing from the superior to the 
inferior conjunction, or from the inferior to the supe- 
rior, through the greatest elongations, the inferior plan- 
ets are stationary. Thus, (Fig. 51,) when the plan- 
et is at A, the earth being at E, as the planet's motion 
is directly towards the spectator, he would constantly 
project it at the same point in the heavens, namely, A'; 
consequently, it would appear to stand still. Or, when 
at its greatest elongation on the other side, at B, as its 
motion would be directly from the spectator, it would 
be seen constantly at B'. If the earth were at rest, the 
stationary points would be at the greatest elongations, 
as at A and B ; but the earth itself is moving nearly at 
right angles to the planet's motion, which makes the 
planet appear to move in the opposite direction. Its 
direct motion will therefore continue longer on the one 
side, and its retrograde motion longer on the other side, 
than would be the case, were it not for the motion of 
the earth. Mercury, whose greatest angular distance 
from the sun is nearly twenty-nine degrees, is station- 
ary at an elongation of from fifteen to twenty degrees ; 
and Venus, at about twenty-nine degrees, although her 
greatest elongation is about forty-seven degrees. 

Mercury and Venus exhibit to the telescope phases 
similar to those of the moon. When on the side of their 
inferior conjunction, as from B to C through D, Fig. 
52, less than half their enlightened disk is turned tow- 
ards us, and they appear horned, like the moon in 
her first and last quarters ; and when on the side of 
the superior conjunction, as from C to B through A, 
more than half the enlightened disk is turned towards 
us, and they appear gibbous. At the moment of su- 
perior conjunction, the whole enlightened orb of the 
planet is turned towards the earth, and the appearance 


would be that of the full moon ; but the planet is too 
near the sun to be commonly visible. 

Fig. 52. 

We should at first thought expect, that each of these 
planets would be largest and brightest near their infe- 
rior conjunction, being then so much nearer to us than 
at other times ; but we must recollect that, when in this 
situation, only a small part of the enlightened disk is 
turned toward us. Still, the period of greatest bril- 
liancy cannot be when most of the illuminated side is 
turned towards us, for then, being at the superior con- 
junction, its light will be diminished, both by its great 
distance, and by its being so near the sun as to be 
partially lost in the twilight. Hence, when Venus is a 
little within her place of greatest elongation, about for- 
ty degrees from the sun, although less than half her disk 
is enlightened, yet, being comparatively near to us, and 
shining at a considerable altitude after the evening or 
before the morning twilight, she then appears in great- 
est splendor, and presents an object admired for its 
beauty in all ages. Thus Milton, 

*' Fairest of stars, last in the train of night, 
If better thou belong not to the dawn, 
Sure pledge of day that crown'st the smiling morn 
With thy bright circlet." 

Mercury and Venus both revolve on their axes in 
nearly the same time with the earth. The diurnal pe- 
riod of Mercury is a little greater, and that of Venus a 
little less, than twenty-four hours. These revolutions 


have been determined by means of some spot or mark 
seen by the telescope, as the revolution of the sun on 
his axis is ascertained by means of his spots. Mercury 
owes most of its peculiarities to its proximity to the sun. 
Its light and heat, derived from the sun, are estimated 
to be nearly seven times as great as on the earth, and 
the apparent magnitude of the sun to a spectator on 
Mercury would be seven times greater than to us. 
Hence the sun would present to an inhabitant of that 
planet, with eyes like ours, an object of insufferable 
brightness ; and all objects on the surface would be 
arrayed in a light more glorious than we can well imag- 
ine. (See Fig. 53.) The average heat on the greater 
portion of this planet would exceed that of boiling wa- 
ter, and therefore be incompatible with the existence 
both of an animal and a vegetable kingdom constituted 
like ours. 

The motion of Mercury, in his revolution round the 
sun, is swifter than that of any other planet, being more 
than one hundred thousand miles every hour ; whereas 
that of the earth is less than seventy thousand. Eigh- 
teen hundred miles every minute, crossing the Atlan- 
tic ocean in less than two minutes, this is a velocity 
of which we can form but a very inadequate conception, 
although, as we shall see hereafter, it is far less than 
comets sometimes exhibit. 

Venus is regarded as the most beautiful of the plan- 
ets, and is well known as the morning and evening 
star. The most ancient nations, indeed, did not recog- 
nise the morning and evening star as one and the same 
body, but supposed they were different planets, and 
accordingly gave them different names, calling the 
morning star Lucifer, and the evening star Hesperus. 
At her period of greatest splendor, Venus casts a shad- 
ow, and is sometimes visible in broad daylight. Her 
light is then estimated as equal to that of twenty stars 
of the first magnitude. In the equatorial regions of the 
earth, where the twilight is short, and Venus, at her 
greatest elongation, appears very high above the hori- 

Fiu. 53. 

rom the 






Figures 54, 55, 56. 



zon, her splendors are said to be far more conspicuous 
than in our latitude. 

Every eight years, Venus forms her conjunction with 
the sun in the same part of the heavens. Whatever 
appearances, therefore, arise from her position with re- 
spect to the earth and the sun, they are repeated every 
eight years, in nearly the same form. 

Thus, every eight years, Venus is remarkably con- 
spicuous, so as to be visible in the day-time, being then 
most favorably situated, on several accounts ; namely, 
being nearest the earth, and at the point in her orbit 
where she gives her greatest brilliancy, that is, a little 
within the place of greatest elongation. This is the pe- 
riod for obtaining fine telescopic views of Venus, when 
she is seen with spots on her disk. Thus two figures 
of the annexed diagram (Fig. 54) represent Venus as 
seen near her inferior conjunction, and at the period of 
maximum brilliancy. The former situation is favora- 
ble for viewing her inequalities of surface, as indicated 
by the roughness of the line which separates the en- 
lightened from the unenlightened part, (the termina- 
tor.) According to Schroeter, a German astronomer, 
Venus has mountains twenty-two miles high. Her 
mountains, however, are much more difficult to be seen 
than those of the moon. 

The sun would appear, as seen from Venus, twice 
as large as on the earth, and its light and heat would 
be augmented in the same proportion. (See Fig. 53.) 
In many respects, however, the phenomena of this 
planet are similar to those of our own ; and the gene- 
ral likeness between Venus and the earth, in regard to 
dimensions, revolutions, and seasons, is greater than 
exists between any other two bodies of the system. 

I will only add to the present Letter a few words on 
the transits of the inferior planets. 

The transit of Mercury or Venus is its passage across 
the sun's disk, as the moon passes over it in a solar 
eclipse. The planet is seen projected on the sun's 
disk in a small, black, round spot, moving slowly over 


the face of the sun. As the transit takes place only 
when the planet is in inferior conjunction, at which 
time her motion is retrograde, it is always from left to 
right ; and, on account of its motion being retarded by 
the motion of the earth, (as was explained by Fig. 51, 
page 232,) it remains sometimes a long time on the solar 
disk. Mercury, when it makes its transit across the sun's 
centre, may remain on the sun from five to seven hours. 
You may ask, why we do not observe this appear- 
ance every time one of the inferior planets comes into 
inferior conjunction, for then, of course, it passes be- 
tween us and the sun. It must, indeed, at this time, 
cross the meridian at the same time with the sun ; but, 
because its orbit is inclined to that of the sun, it may 
cross it (and generally does) a little above or a little be- 
low the sun. It is only when the conjunction takes 
place at or very near the point where the two orbits cross 
one another, that is, near the node, that a transit can 
occur. Thus, if the orbit of Mercury, N M R, Fig. 50, 
(page 231,) were in the same plane with the earth's or- 
bit, (and of course with the sun's apparent orbit,) then, 
when the planet was at Q,, in its inferior conjunction, 
the earth being at E, it would always be projected on 
the sun's disk at Z, on the concave sphere of the heav- 
ens, and a transit would happen at every inferior con- 
junction. But now let us take hold of the point R, 
and lift the circle which represents the orbit of Mercu- 
ry upwards seven degrees, letting it turn upon the diam- 
eter d b ; then, we may easily see that a spectator at E 
would project the planet higher in the heavens than 
the sun ; and such would always be the case, except 
when the conjunction takes place at the node. Then 
the point of intersection of the two orbits being in one 
and the same plane, both bodies would be referred to 
the same point on the celestial sphere. As the sun, 
in his apparent revolution around the earth every year, 
passes through every point in the ecliptic, of course 
he must every year be at each of the points where the 
orbit of Mercury or Venus crosses the ecliptic, that is, 


at eacl> of the nodes of one of these planets ;* and as 
these nodes are on opposite sides of the ecliptic, con- 
sequently, the sun will pass through them at opposite 
seasons of the year, as in January and July, February 
and August. Now, should Mercury or Venus happen 
to come between us and the sun, just as the sun is pass- 
ing one of the planet's nodes, a transit would happen. 
Hence the transits of Mercury take place in May and 
November, and those of Venus, in June and December. 

Transits of Mercury occur more frequently than 
those of Venus. The periodic times of Mercury and 
the earth are so adjusted to each other, that Mercury 
performs nearly twenty-nine revolutions while the earth 
performs seven. If, therefore, the two bodies meet at 
the node in any given year, seven years afterwards they 
will meet nearly at the same node, and a transit may 
take place, accordingly, at intervals of seven years. 
But fifty-four revolutions of Mercury correspond still 
nearer to thirteen revolutions of the earth ; and there- 
fore a transit is still more probable after intervals of thir- 
teen years. At intervals of thirty-three years, transits 
of Mercury are exceedingly probable, because in that 
time Mercury makes almost exactly one hundred and 
thirty-seven revolutions. Intermediate transits, howev- 
er, may occur at the other node. Thus, transits of 
"Mercury happened at the ascending node in 1815, and 
1822, at intervals of seven years ; and at the descend- 
ing node in 1832, which will return in 1845, after thir- 
teen years. 

Transits of Venus are events of very unfrequent oc- 
currence. Eight revolutions of the earth are com- 
pleted in nearly the same time as thirteen revolutions 
of Venus ; and hence two transits of Venus may oc- 
cur after an interval of eight years, as was the case at 
the last return of the phenomenon, one transit having 
occurred in 1761, and another in 1769. But if a tran- 

* You will recollect that the sun is said to be at the node, when 
the places of the node and the sun are both projected, by a spectator 
on the earth, upon the same part of the heavens. 


sit does not happen after eight years, it will not happen 
at the same node, until an interval of two hundred and 
thirty-five years : but intermediate transits may occur a; 
the other node. The next transit of Venus will tak 
place in 1874, being two hundred and thirty-five year 
after the first that was ever observed, which occurred 
in 1639. This was seen, for the first time by morta 
eyes, by two youthful English astronomers, Horrox 
and Crabtree. Horrox was a young man of extraor- 
dinary promise, and indicated early talents for prac- 
tical astronomy, which augured the highest eminence ; 
but he died in the twenty-third year of his age. He 
was only twenty when the transit appeared, and he had 
made the calculations and observations, by which he 
was enabled to anticipate its arrival several years before. 
At the approach of the desired time for observing the 
transit, he received the sun's image through a telescope 
in a dark room upon a white piece of paper, and after 
waiting many hours with great impatience, (as his cal- 
culation did not lead him to a knowledge of the precise 
time of the occurrence,) at last, on the twenty-fourth of 
November, 1639, old style, at three and a quarter 
hours past twelve, just as he returned from church, he 
had the pleasure to find a large round spot near the limb 
of the sun's image. It moved slowly across the sun's 
disk, but had not entirely left it when the sun set. 

The great interest attached by astronomers to a 
transit of Venus arises from its furnishing the most ac- 
curate means in our power of determining the surfs 
horizontal parallax, an element of great importance, 
since it leads us to a knowledge of the distance of the 
earth from the sun, which again affords the means of 
estimating the distances of all the other planets, and 
possibly, of the fixed stars. Hence, in 1769, great ef- 
forts were made throughout the civilized world, under 
the patronage of different governments, to observe this 
phenomenon under circumstances the most favorable 
for determining the parallax of the sun. 

The common methods of finding the parallax of a 


heavenly body cannot be relied on to a greater degree 
of accuracy than four seconds. In the case of the 
moon, whose greatest parallax amounts to about one 
legree, this deviation from absolute accuracy is not 
very material ; but it amounts to nearly half the entire 
parallax of the sun. 

If the sun and Venus were equally distant from us, 
they would be equally affected by parallax, as viewed 
by spectators in different parts of the earth, and hence 
their relative situation would not be altered by it ; but 
since Venus, at the inferior conjunction, is only about 
one third as far off as the sun, her parallax is pro- 
portionally greater, and therefore spectators at distant 
points will see Venus projected on different parts of the 
solar disk, as the planet traverses the disk. Astrono- 
mers avail themselves of this circumstance to ascertain 
the sun's horizontal parallax, which they are enabled to 
do by comparing it with that of Venus, in a manner 
which, without a knowledge of trignometry, you will 
not fully understand. In order to make the difference 
in the apparent places of Venus on the sun's disk as 
great as possible, very distant places are selected for 
observation. Thus, in the transits of 1761 and 1769, 
several of the European governments fitted out expen- 
sive expeditions to parts of the earth remote from each 
other. For this purpose, the celebrated Captain Cook, 
in 1769, went to the South Pacific Ocean, and observ- 
ed the transit at the island of Otaheite, while others 
went to Lapland, for the same purpose, and others still, 
to many other parts of the globe. Thus, suppose two 
observers took their stations on opposite sides of the 
earth, as at A, and B, Fig. 57, page 242; at A, the 
planet V would be seen on the sun's disk at a, while 
at B, it would be seen at b. 

The appearance of Venus on the sun's disk being 
that of a well-defined black spot, and the exactness 
with which the moment of external or internal contact 
may be determined, are circumstances favorable to the 
exactness of the result ; and astronomers repose so- 

21 L. A. 



Fig. 57. much confidence in the estimation of 
the sun's horizontal parallax, as de- 
rived from observations on the transit 
of 1769, that this important element is 
thought to be ascertained within one 
tenth of a second. The general re- 
sult of all these observations gives the 
sun's horizontal parallax eight seconds 
and six tenths, a result which shows 
at once that the sun must be a great 
way off, since the semidiameter of the 
earth, a line nearly four thousand miles 
in length, would appear at the sun un- 
der an angle less than one four hun- 
dredth of a degree. During the tran- 
sits of Venus over the sun's disk, in 
1761 and 1769, a sort of penumbral 
light was observed around the plan- 
et, by several astronomers, which was 
thought to indicate an atmosphere. 
This appearance was particularly ob- 
servable while the planet was coming 
on or going off the solar disk. The 
total immersion and emersion were not 
instantaneous ; but as two drops of 
water, when about to separate, form a 
ligament between them, so there was 
a dark shade stretched out between Venus and the 
sun ; and when the ligament broke, the planet seemed 
to have got about an eighth part of her diameter from 
the limb of the sun. The various accounts of the two 
transits abound with remarks like these, which indicate 
the existence of an atmosphere about Venus of near- 
ly the density and extent of the earth's atmosphere. 
Similar proofs of the existence of an atmosphere around 
this planet are derived from appearances of twilight. 

The elder astronomers imagined that they had dis- 
covered a satellite accompanying Venus in her transit. 
If Venus had in reality any satellite, the fact would 


be obvious at her transits, as, in some of them at least, 
it is probable that the satellite would be projected near 
the primary on the sun's disk ; but later astronomers 
have searched in vain for any appearances of the kind, 
and the inference is, that former astronomers were de- 
ceived by some optical illusion. 



" With what an awful, world-revolving power, 
Were first the unwieldy planets launched along 
The illimitable void ! There to remain 
Amidst the flux of many thousand years, 
That oft has swept the toiling race of men, 
And all their labored monuments, away." Thomson. 

MERCURY AND VENUS, as we have seen, are always 
observed near the sun, and from this circumstance, as 
well as from the changes of magnitude and form which 
they undergo, we know that they have their orbits 
within that of the earth, and hence we call them infe- 
rior planets. On the other hand, Mars, Jupiter, Sa- 
turn, and Uranus, exhibit such appearances, at different 
times, as show that they revolve around the sun at a 
greater distance than the earth, and hence we denomi- 
nate them superior planets. We know that they nev- 
er come between us and the sun, because they never 
undergo those changes which Mercury and Venus, as 
well as the moon, sustain, in consequence of their com- 
ing into such a position. They, however, wander to 
the greatest angular distance from the sun, being some- 
times seen one hundred and eighty degrees from him, 
so as to rise when the sun sets. All these different, 
appearances must naturally result from their orbits' be- 
ing exterior to that of the earth, as will be evident from 
the following representation. Let E, Fig. 58, page 244, 
be the earth, and M, one of the superior planets, Mars, 
for example, each body being seen in its path around the 


Fig. 58. 

sun. At M, the planet would be in opposition to the 
sun, like the moon at the full ; at Q,, and Q,', it would be 
seen ninety degrees off, or in quadrature ; and at M', in 
conjunction. We know, however, that this must be a 
superior and not an inferior conjunction, for the illumi- 
nated disk is still turned towards us ; whereas, if it came 
between us and the sun, like Mercury, or Venus, in its 
inferior conjunction, its dark side would be presented 
to us. 

The superior planets do not exhibit to the telescope 
different phases, but, with a single exception, they al- 
ways present the side that is turned towards the earth 
fully enlightened. This is owing to their great dis- 
tance from the earth ; for were the spectator to stand 
upon the sun, he would of course always have the illu- 
minated side of each of the planets turned towards 
him ; but so distant are all the superior planets, except 
Mars, that they are viewed by us very nearly in the 
same manner as they would be if we actually stood on 
the sun. Mars, however, is sufficiently near to appear 
somewhat gibbous when at or near one of its quadra- 
tures. Thus, when the planet is at Q, it is plain that, 


of the hemisphere that is turned towards the earth, a 
small part is unilluminated. 

MARS is a small planet, his diameter being only about 
half that of the earth, or four thousand two hundred 
miles. He also, at times, comes nearer to the earth 
than any other planet, except Venus. His mean dis- 
tance from the sun is one hundred and forty-two mil- 
lions of miles ; but his orbit is so elliptical, that his dis- 
tance varies much in different parjts of his revolution. 
Mars is always very near the ecliptic, never varying 
from it more than two degrees. He is distinguished 
from all the planets by his deep red color, and fiery as- 
pect ; but his brightness and apparent magnitude vary 
much, at different times, being sometimes nearer to us 
than at others by the whole diameter of the earth's or- 
bit ; that is, by about one hundred and ninety millions 
of miles. When Mars is on the same side of the sun 
with the earth, or at his opposition, he comes within 
forty-seven millions of miles of the earth, and, rising 
about the time the sun sets, surprises us by his magni- 
tude and splendor ; but when he passes to the other 
side of the sun, to his superior conjunction, he dwindles 
to the appearance of a small star, being then two hun- 
dred and thirty-seven millions of miles from us. Thus, 
let M, Fig, 58, represent Mars in opposition, and M', in 
the superior conjunction, while E represents the earth. 
It is obvious that, in the former situation, the planet 
must be nearer to the earth than in the latter, by the 
whole diameter of the earth's orbit. When viewed with 
a powerful telescope, the surface of Mars appears di- 
versified with numerous varieties of light and shade. 
The region around the poles is marked by white spots, 
(see Fig. 56, page 237,) which vary their appearances 
with the changes of seasons in the planet. Hence Dr. 
Herschel conjectured that they were owing to ice and 
snow, which alternately accumulate and melt away, 
according as it is Winter or Summer, in that region. 
They are greatest and most conspicuous when that part 
of the planet has just emerged from a long- Winter, and 


they gradually waste away, as they are exposed to the 
solar heat. Fig. 56, represents the planet, as exhibited, 
under the most favorable circumstances, to a powerful 
telescope, at the time when its gibbous form is striking- 
ly obvious. It has been common to ascribe the ruddy 
light of Mars to an extensive and dense atmosphere, 
which was said to be distinctly indicated by the gradual 
diminution of light observed in a star, as it approaches 
very near to the planet, in undergoing an occultation ; 
but more recent observations afford no such evidence 
of an atmosphere. 

By observations on the spots, we learn that Mars re- 
volves on his axis in very nearly the same time with the 
earth, (twenty-four hours thirty-nine minutes twenty-one 
seconds and three tenths,) and that the inclination of 
his axis to that of his orbit is also nearly the same, be- 
ing thirty degrees eighteen minutes ten seconds and 
eight tenths. Hence the changes of day and night 
must be nearly the same there as here, and the seasons 
also very similar to ours. Since, however, the distance 
of Mars from the sun is one hundred and forty-two 
while that of the earth is only ninety-five millions of 
miles, the sun will appear more than twice as small on 
that planet as on ours, (see Fig. 53, page 236,) and its 
light and heat will be diminished in the same propor- 
tion. Only the equatorial regions, therefore, will be 
suitable for the existence of animals and vegetables. 

The earth will be seen from Mars as an inferior plan- 
et, always near the sun, presenting appearances similar, 
in many respects, to those which Venus presents to us. 
It will be to that planet the evening and morning star, 
sung by their poets (if poets they have) with a like en- 
thusiasm. The moon will attend the earth as a little 
star, being never seen further from her side than about 
the diameter under which we view the moon. To the 
telescope, the earth will exhibit phases similar to those 
of Venus ; and, finally, she will, at long intervals, make 
her transits over the solar disk. Mean-while, Venus will 
stand to Mars in a relation similar to that of Mercury 


to us, revealing herself only when at the periods of her 
greatest elongation, and at all other times hiding her- 
self within the solar blaze. Mercury will never be vis- 
ible to an inhabitant of Mars. 

JUPITER is distinguished from all the other planets 
by his great magnitude. His diameter is eighty-nine 
thousand miles, and his volume one thousand two hun- 
dred and eighty times that of the earth, s His figure is 
strikingly spheroidal, the equatorial being more than 
six thousand miles longer than the polar diameter. 
Such a figure might naturally be expected from the 
rapidity of his diurnal rotation, which is accomplished 
in about ten hours. A place on the equator of Jupiter 
must turn twenty-seven times as fast as on the terres- 
trial equator. The distance of Jupiter from the sun is 
nearly four hundred and ninety millions of miles, and 
his revolution around the sun occupies nearly twelve 
years. Every thing appertaining to Jupiter is on a grand 
scale. A world in itself, equal in dimensions to twelve 
hundred and eighty of ours ; the whole firmament roll- 
ing round it in the short space of ten hours, a move- 
ment so rapid that the eye could probably perceive the 
heavenly bodies to change their places every moment ; 
its year dragging out a length of more than four thous- 
and days, and more than ten thousand of its own days, 
while its nocturnal skies are lighted up with four bril- 
liant moons ; these are some of the peculiarities which 
characterize this magnificent planet. 

The view of Jupiter through a good telescope is one 
of the most splendid and interesting spectacles in astron- 
omy. The disk expands into a large and bright orb, 
like the full moon ; the spheroidal figure which theory 
assigns to revolving spheres, especially to those which 
turn with great velocity, is here palpably exhibited to 
the eye ; across the disk, arranged in parallel stripes, 
are discerned several dusky bands, called belts ; and 
four bright satellites, always in attendance, and ever va- 
rying their positions, compose a splendid retinue. In- 
deed, astronomers gaze with peculiar interest on Jupiter 


and his moons, as affording a miniature representation 
of the whole solar system, repeating, on a smaller scale, 
the same revolutions, and exemplifying more within the 
compass of our observation, the same laws as regulate 
the entire assemblage of sun and planets. Figure 59, 
facing page 247, gives a correct view of Jupiter, as ex- 
hibited to a powerful telescope in a clear evening. You 
will remark his flattened or spheroidal figure, the belts 
which appear in parallel stripes across his disk, and the 
four satellites, that are seen like little stars in a straight 
line with the equator of the planet. 

The belts of Jupiter are variable in their number 
and dimensions. With the smaller telescopes only one 
or two are seen, and those across the equatorial regions ; 
but with more powerful instruments, the number is in- 
creased, covering a large part of the entire disk. Dif- 
ferent opinions have been entertained by astronomers 
respecting the cause of these belts ; but they have gen- 
erally been regarded as clouds formed in the atmos- 
phere of the planet, agitated by winds, as is indicated 
by their frequent changes, and made to assume the 
form of belts parallel to the equator, like currents that 
circulate around our globe. Sir John Herschel sup- 
poses that the belts are not ranges of clouds, but por- 
tions of the planet itself, brought into view by the re- 
moval of clouds and mists, that exist in the atmosphere 
of the planet, through which are openings made by 
currents circulating around Jupiter. 

The satellites of Jupiter may be seen with a tele- 
scope of very moderate powers. Even a common spy- 
glass will enable us to discern them. Indeed, one or 
two of them have been occasionally seen with the na- 
ked eye. In the largest telescopes they severally ap- 
pear as bright as Sirius. With such an instrument, 
the view of Jupiter, with his moons and belts, is truly 
a magnificent spectacle. As the orbits of the satellites 
do not deviate far from the plane of the ecliptic, and 
but little from the equator of the planet, they are us- 
ually seen in nearly a straight line with each other, ex- 


tending across the central part of the disk. (See Fig. 
59, facing page 247.) 

Jupiter and his satellites exhibit in miniature all the 
phenomena of the solar system. The satellites per- 
form, around their primary, revolutions very analogous 
to those which the planets perform around the sun, 
having, in like manner, motions alternately direct, sta- 
tionary, and retrograde. They are all, with one excep- 
tion, a little larger than the moon ; and the second sat- 
ellite, which is the smallest, is nearly as large as the 
moon, being two thousand and sixty-eight miles in di- 
ameter. They are all very small compared with the 
primary, the largest being only one twenty-sixth part 
of the primary. The outermost satellite extends to 
the distance from the planet of fourteen times his di- 
ameter. The whole system, therefore, occupies a re- 
gion of space more than one million miles in breadth. 
Rapidity of motion, as well as greatness of dimensions, 
is characteristic of the system of Jupiter. I have al- 
ready mentioned that the planet itself has a motion on 
its own axis much swifter than that of the earth, and 
the motions of the satellites are also much more rapid 
than that of the moon. The innermost, which is a 
little further off than the moon is from the earth, goes 
round its primary in about a day and three quarters ; 
and the outermost occupies less than seventeen days. 

The orbits of the satellites are nearly or quite circu- 
lar, and deviate but little from the plane of the plari- 
et's equator, and of course are but slightly inclined to 
the plane of his orbit. They are therefore in a similar 
situation with respect to Jupiter, as the moon would be 
with respect to the earth, if her orbit nearly coincided 
with the ecliptic, in which case, she would undergo an 
eclipse at every opposition. The eclipses of Jupiter's 
satellites, in their general circumstances, are perfectly 
analogous to those of the moon, but in their details 
they differ in several particulars. Owing to the much 
greater distance of Jupiter from the sun, and its great- 
er magnitude, the cone of its shadow is much longer 


and larger than that of the earth. On this account, 
as well as on account of the little inclination of their 
orbit to that of the primary, the three inner satellites 
of Jupiter pass through his shadow, and are totally 
eclipsed, at every revolution. The fourth satellite, ow- 
ing to the greater inclination of its orbit, sometimes, 
though rarely, escapes eclipse, and sometimes merely 
grazes the limits of the shadow, or suffers a partial 
eclipse. These eclipses, moreover, are not seen, as is 
the case with those of the moon, from the centre of 
their motion, but from a remote station, and one whose 
situation with respect to the line of the shadow is vari- 
able. This makes no difference in the times of the 
eclipses, but it makes a very great one in their visibili- 
ty, and in their apparent situations with respect to the 
planet at the moment of their entering or quitting the 

The eclipses of Jupiter's satellites present some cu- 
rious phenomena, which you will easily understand by 
studying the following diagram. Let A, B, C, D, Fig. 
61, represent the earth in different parts of its orbit; 
Fig. 61. 

J, Jupiter, in his orbit, surrounded by his four satellites, 
the orbits of which are marked 1, 2, 3, 4. At a, the 
first satellite enters the shadow of the planet, emerges 
from it at b, and advances to its greatest elongation at 
c. The other satellites traverse the shadow in a similar 
manner. The apparent place, with respect to the plan 


marked by Roemer, a Danish astronomer, on compar- 
ing together observations of these eclipses during many 
successive years, that they take place sooner by about 
sixteen minutes, when the earth is on the same side of 
the sun with the planet, than when she is on the oppo- 
site side. The difference he ascribes to the progres- 
sive motion of light, which takes that time to pass 
through the diameter of the earth's orbit, making the 
velocity of light about one hundred and ninety-two 
thousand miles per second. So great a velocity start- 
led astronomers at first, and produced some degree of 
distrust of this explanation of the phenomenon ; but 
the subsequent discovery of what is called the aber- 
ration of light, led to an independent estimation of the 
velocity of light, with almost precisely the same result. 

Few greater feats have ever been performed by the 
human mind, than to measure the speed of light, a 
speed so great, as would carry it across the Atlantic 
Ocean in the sixty-fourth part of a second, and around 
the globe in less than the seventh part of a second ! 
Thus has man applied his scale to the motions of an 
element, that literally leaps from world to world in the 
twinkling of an eye. This is one example of the great 
power which the invention of the telescope conferred 
on man. 

Could we plant ourselves on the surface of this vast 
planet, we should see the same starry firmament ex- 
panding over our heads as we see now ; and the same 
would be true if we could fly from one planetary world 
to another, until we "made the circuit of them all; but 
the sun and the planetary system would present them- 
selves to us under new and strange aspects. The sun 
himself would dwindle to one twenty-seventh of his pres- 
ent surface, (Fig. 53, facing page 236,) and afford a de- 
gree of light and heat proportionally diminished ; Mercu- 
ry, Venus, and even the Earth, would all disappear, being 
too near the sun to be visible ; Mars would be as seldom 
seen as Mercury is by us, and constitute the only inferi- 
or planet. On the other hand, Saturn would shine with 

22 L. A. 


greatly augmented size and splendor. When in oppo- 
sition to the sun, (at which time it comes nearest to Ju- 
piter,) it would be a grand object, appearing larger than 
either Venus or Jupiter does to us. When, however, 
passing to the other side of the sun, through its supe- 
rior conjunction, it would gradually diminish in size and 
brightness, and at length become much less than it ever 
appears to us, since it would then be four hundred mil- 
lions of miles further from Jupiter than it ever is from us. 
Although Jupiter comes four hundred millions of 
miles nearer to Uranus than the earth does, yet it is 
still thirteen hundred millions of miles distant from that 
planet. Hence the augmentation of the magnitude and 
light of Uranus would be barely sufficient to render it 
distinguishable by the naked eye. It appears, there- 
fore, that Saturn is the peculiar ornament of the firma- 
ment of Jupiter, and would present to the telescope most 
interesting and sublime phenomena. As we owe the 
revelation of the system of Jupiter and his attendant 
worlds wholly to the telescope, and as the discovery 
and observation of them constituted a large portion of 
the glory of Galileo, I am now forcibly reminded of his 
labors, and will recur to his history, and finish the sketch 
which I commenced in a previous Letter. 



** They leave at length the nether gloom, and stand 
Before the portals of a better land ; 
To happier plains they come, and fairer groves, 
The seats of those whom Heaven, benignant, loves; 
A brighter day, a bluer ether, spreads 
Its lucid depths above their favored heads ; 
And, purged from mists that veil our earthly skies, 
Shine suns and stars unseen by mortal eyes." Virgil. 

IN order to appreciate the value of the contributions 
which Galileo made to astronomy, soon after the inven- 
tion of the telescope, it is necessary to glance at the 
state of the science when he commenced his discoveries. 


For many centuries, during the middle ages, a dark 
night had hung over astronomy, through which hardly a 
ray of light penetrated, when, in the eastern part of civil- 
ized Europe, a luminary appeared, that proved the har- 
binger of a bright and glorious day. This was Coperni- 
cus, a native of Thorn, in Prussia. He was born in 1473. 
Though destined for the profession of medicine, from 
his earliest years he displayed a great fondness and ge- 
nius for mathematical studies, and pursued them with 
distinguished success in the University of Cracow. At 
the age of twenty-five years, he resorted to Italy, for 
the purpose of studying astronomy, where he resided a 
number of years. Thus prepared, he returned to his 
native country, and, having acquired an ecclesiastical 
living that was adequate to his support in his frugal 
mode of life, he established himself at Frauenberg, a 
small town near the mouth of the Vistula, where he 
spent nearly forty years in observing the heavens, and 
meditating on the celestial motions. He occupied the 
upper part of a humble farm-house, through the roof of 
which he could find access to an unobstructed sky, and 
there he carried on his observations. His instruments, 
however, were few and imperfect, and it does not ap- 
pear that he added any thing to the art of practical as- 
tronomy. This was reserved for Tycho Brahe, who 
came a half a century after him. Nor did Copernicus 
enrich the science with any important discoveries. It 
was not so much his genius or taste to search for new 
bodies, or new phenomena among the stars, as it was 
to explain the reasons of the most obvious and well- 
known appearances and motions of the heavenly bo- 
dies. With this view, he gave his mind to long-con- 
tinued and profound meditation. 

Copernicus tells us that he was first led to think that 
the apparent motions of the heavenly bodies, in their 
diurnal revolution, were owing to the real motion of the 
earth in the opposite direction, from observing instances 
of the same kind among terrestrial objects ; as when the 
shore seems to the mariner to recede, as he rapidly sails 


from it ; and as trees and other objects seem to glide by 
us, when, on riding swiftly past them, we lose the 
consciousness of our own motion. He was also smitten 
with the simplicity prevalent in all the works and op- 
erations of Nature, which is more and more conspicuous 
the more they are understood ; and he hence concluded 
that the planets do not move in the complicated paths 
which most preceding astronomers assigned to them. I 
shall explain to you, hereafter, the details of his system. 
I need only at present remind you that the hypothesis 
which he espoused and defended, (being substantially 
the same as that proposed by Pythagoras, five hundred 
years before the Christian era,) supposes, first, that the 
apparent movements of the sun by day, and of the moon 
and stars by night, from east to west, result from the 
actual revolution of the earth on its own axis from west 
to east ; and, secondly, that the earth and all the planets 
revolve about the sun in circular orbits. This hypothe- 
sis, when he first assumed it, was with him, as it had 
been with Pythagoras, little more than mere conjecture. 
The arguments by which its truth was to be finally 
established were not yet developed, and could not be, 
without the aid of the telescope, which was not yet in- 
vented. Upon this hypothesis, however, he set out to 
explain all the phenomena of the visible heavens, as 
the diurnal revolutions of the sun, moon, and stars, the 
slow progress of the planets through the signs of the zo- 
diac, and the numerous irregularities to which the plan- 
etary motions are subject. These last are apparently so 
capricious, being for some time forward, then station- 
ary, then backward, then stationary again, and finally 
direct, a second time, in the order of the signs, and con- 
stantly varying in the velocity of their movements, that 
nothing but long-continued and severe meditation could 
have solved all these appearances, in conformity with the 
idea that each planet is pursuing its simple way all the 
while in a circle around the sun. Although, therefore, 
Pythagoras fathomed the profound doctrine that the sun 
is the centre around which the earth and all the planets 


revolve, yet we have no evidence that he ever solved 
the irregular motions of the planets in conformity with 
his hypothesis, although the explanation of the diurnal 
revolution of the heavens, by that hypothesis, involved 
no difficulty. Ignorant as Copernicus was of the prin- 
ciple of gravitation, and of most of the laws of motion, 
he could go but little way in following out the conse- 
quences of his own hypothesis ; and all that can be 
claimed for him is, that he solved, by means of it, most 
of the common phenomena of the celestial motions. 
He indeed got upon the road to truth, and advanced 
some way in its sure path ; but he was able to adduce 
but few independent proofs, to show that it was the 
truth. It was only quite at the close of his life that he 
published his system to the world, and that only at the 
urgent request of his friends ; anticipating, perhaps, the 
opposition of a bigoted priesthood, whose ifury was af- 
terwards poured upon the head of Galileo, for main- 
taining the same doctrines. 

Although, therefore, the system of Copernicus afford- 
ed an explanation of the celestial motions, far more 
simple and rational than the previous systems which 
made the earth the centre of those motions, yet this 
fact alone was not sufficient to compel the assent of 
astronomers ; for the greater part, to say the least, of 
the same phenomena, could be explained on either hy- 
pothesis. With the old doctrine astronomers were al- 
ready familiar, a circumstance which made it seem easi- 
er ; while the new doctrines would seem more difficult, 
from their being imperfectly understood. Accordingly, 
for nearly a century after the publication of the system of 
Copernicus, he gained few disciples. Tycho Brahe re- 
jected it, and proposed one of his own, of which I shall 
hereafter give you some account ; and it would proba- 
bly have fallen quite into oblivion, had not the obser- 
vations of Galileo, with his newly-invented telescope, 
brought to light innumerable proofs of its truth, far more 
cogent than any which Copernicus himself had been 
able to devise. 



Galileo no sooner had completed his telescope, and 
directed it to the heavens, than a world of wonders sud- 
denly burst upon his enraptured sight. Pointing it to 
the moon, he was presented with a sight of her mottled 
disk, and of her mountains and valleys. The sun ex- 
hibited his spots ; Venus, her phases ; and Jupiter, his 
expanded orb, and his retinue of moons. These last 
he named, in honor of his patron, Cosmo d'Medici, Med- 
icean stars. So great was this honor deemed of asso- 
ciating one's name with the stars, that express applica- 
tion was made to Galileo, by the court of France, to 
award this distinction to the reigning Monarch, Henry 
the Fourth, with plain intimations, that by so doing he 
would render himself and his family rich and powerful 
for ever. 

Galileo published the result of his discoveries in a pa- 
per, denominated ' Nuncius Sidereus' the ' Messenger 
of the Stars.' In that ignorant and marvellous age, this 
publication produced a wonderful excitement. " Many 
doubted, many positively refused to believe, so novel an 
announcement ; all were struck with the greatest aston- 
ishment, according to their respective opinions, either at 
the new view of the universe thus offered to them, or at 
the high audacity of Galileo, in inventing such fables." 
Even Kepler, the great German astronomer, of whom I 
shall tell you more by and by, wrote to Galileo, and de- 
sired him to supply him with arguments, by which he 
might answer the objections to these pretended discov- 
eries with which he was continually assailed. Galileo 
answered him as follows : " In the first place, I return 
you my thanks that you first, and almost alone, before 
the question had been sifted, (such is your candor, and 
the loftiness of your mind,) put faith in my assertions. 
You tell me you have some telescopes, but not sufficient- 
ly good to magnify distant objects with clearness, and 
that you anxiously expect a sight of mine, which mag- 
nifies images more than a thousand times. It is mine 
no longer, for the Grand Duke of Tuscany has asked it 
of me, and intends to lay it up in his museum, among 


his most rare and precious curiosities, in eternal remem- 
brance of the invention. 

" You ask, my dear Kepler, for other testimonies. I 
produce, for one, the Grand Duke, who, after observing 
the Medicean planets several times with me at Pisa, 
during the last months, made me a present, at parting, 
of more than a thousand florins, and has now invited 
me to attach myself to him, with the annual salary of one 
thousand florins, and with the title of ' Philosopher and 
Principal Mathematician to His Highness ;' without the 
duties of any office to perform, but with the most com- 
plete leisure. I produce, for another witness, myself, 
who, although already endowed in this College with the 
noble salary of one thousand florins, such as no profes- 
sor of mathematics ever before received, and which I 
might securely enjoy during my life, even if these plan- 
ets should deceive me and should disappear, yet quit 
this situation, and take me where want and disgrace 
will be my punishment, should I prove to have been 

The learned professors in the universities, who, in 
those days, were unaccustomed to employ their senses 
in inquiring into the phenomena of Nature, but satisfied 
themselves with the authority of Aristotle, on all sub- 
jects, were among the most incredulous with respect to 
the discoveries of Galileo. " Oh, my dear Kepler," 
says Galileo, " how I wish that we could have one 
hearty laugh together. Here, at Padua, is the princi- 
pal Professor of Philosophy, whom I have repeatedly 
and urgently requested to look at the moon and planets 
through my glass, which he pertinaciously refuses to do. 
Why are you not here ? What shouts of laughter we 
should have at this glorious folly, and to hear the Pro- 
fessor of Philosophy at Pisa laboring before the Grand 
Duke, with logical arguments, as if with magical incan- 
tations, to charm the new planets out of the sky." 

The following argument by Sizzi, a contemporary 
astronomer of some note, to prove that there can be 
only seven planets, is a specimen of the logic with 


which Galileo was assailed. " There are seven win- 
dows given to animals in the domicile of the head, 
through which the air is admitted to the tabernacle of 
the body, to enlighten, to warm, and to nourish it ; 
which windows are the principal parts of the microcosm, 
or little world, two nostrils, two eyes, two ears, and 
one mouth. So in the heavens, as in a macrocosm, or 
great world, there are two favorable stars, Jupiter and 
Venus ; two unpropitious, Mars and Saturn ; two lu- 
minaries, the Sun and Moon ; and Mercury alone, un- 
decided and indifferent. From which, and from many 
other phenomena of Nature, such as the seven metals, 
&c., which it were tedious to enumerate, we gather 
that the number of planets is necessarily seven. More- 
over, the satellites are invisible to the naked eye, and 
therefore can exercise no influence over the earth, and 
therefore would be useless, and therefore do not exist. 
Besides, as well the Jews and other ancient nations, as 
modern Europeans, have adopted the division of the 
week into seven days, and have named them from the 
seven planets. Now, if we increase the number of 
planets, this whole system falls to the ground." 

When, at length, the astronomers of the schools 
found it useless to deny the fact that Jupiter is attend- 
ed by smaller bodies, which revolve around him, they 
shifted their ground of warfare, and asserted that Gali- 
leo had not told the whole truth ; that there were not 
merely four satellites, but a still greater number ; one 
said five ; another, nine ; and another, twelve ; but, in a 
little time, Jupiter moved forward in his orbit, and left 
all behind him, save the four Medicean stars. 

It had been objected to the Copernican system, that 
were Venus 'a body which revolved around the sun in 
an orbit interior to that of the earth, she would undergo 
changes similar to those of the moon. As no such 
changes could be detected by the naked eye, no satis- 
factory answer could be given to this objection ; but 
the telescope set all right, by showing, in fact, the pha- 
ses of Venus. The same instrument disclosed, also, in 


the system of Jupiter and his moons, a miniature exhi- 
bition of the solar system itself. It showed the actual 
existence of the motion of a number of bodies around 
one central orb, exactly similar to that which was pred- 
icated of the sun and planets. Every one, therefore, 
of these new and interesting discoveries, helped to con- 
firm the truth of the system of Copernicus. 

But a fearful cloud was now rising over Galileo, which 
spread itself, and grew darker every hour. The Church 
of Rome had taken alarm at the new doctrines respect- 
ing the earth's motion, as contrary to the declarations 
of the Bible, and a formidable difficulty presented it- 
self, namely, how to publish and defend these doctrines, 
without invoking the terrible punishments inflicted by 
the Inquisition on heretics. No work could be printed 
without license from the court of Rome ; and any opin- 
ions supposed to be held and much more known to 
be taught by any one, which, by an ignorant and su- 
perstitious priesthood, could be interpreted as contrary 
to Scripture, would expose the offender to the sever- 
est punishments, even to imprisonment, scourging, and 
death. We, who live in an age so distinguished for 
freedom of thought and opinion, can form but a very 
inadequate conception of the bondage in which the 
minds of men were held by the chains of the Inquisi- 
tion. It was necessary, therefore, for Galileo to pro- 
ceed with the greatest caution in promulgating truths 
which his own discoveries had confirmed. He did not, 
like the Christian martyrs, proclaim the truth in the 
face of persecutions and tortures ; but while he sought 
to give currency to the Copernican doctrines, he labor- 
ed, at the same time, by cunning artifices, to blind the 
ecclesiastics to his real designs, and thus to escape the 
effects of their hostility. 

Before Galileo published his doctrines in form, he had 
expressed himself so freely, as to have excited much 
alarm among the ecclesiastics. One of them preached 
publicly against him, taking for his text, the passage, 
" Ye men of Galilee, why stand ye here gazing up into 


heaven ?" He therefore thought it prudent to resort to 
Rome, and confront his enemies face to face. A con- 
temporary describes his appearance there in the follow- 
ing terms, in a letter addressed to a Romish Cardinal : 
" Your Eminence would be delighted with Galileo, if 
you heard him holding forth, as he often does, in the 
midst of fifteen or twenty, all violently attacking him, 
sometimes in one house, sometimes in another. But 
he is armed after such fashion, that he laughs all of 
them to scorn ; and even if the novelty of his opinions 
prevents entire persuasion, at least he convicts of emp- 
tiness most of the arguments with which his adversaries 
endeavor to overwhelm him." 

In 1616, Galileo, as he himself states, had a most 
gracious audience of the Pope, Paul the Fifth, which 
lasted for nearly an hour, at the end of which his Holi- 
ness assured him, that the Congregation were no longer 
in a humor to listen lightly to calumnies against him, 
and that so long as he occupied the Papal chair, Gali- 
leo might think himself out of all danger. Neverthe- 
less, he was not allowed to return home, without receiv- 
ing formal notice not to teach the opinions of Coper- 
nicus, " that the sun is in the centre of the system, and 
that the earth moves about it," from that time forward, 
in any manner. 

Galileo had a most sarcastic vein, and often rallied 
his persecutors with the keenest irony. This he ex- 
hibited, some time after quitting Rome, in an epistle 
which he sent to the Arch Duke Leopold, accompany- 
ing his 'Theory of the Tides.' "This theory," says 
he, " occurred to me when in Rome, whilst the the- 
ologians were debating on the prohibition of Coperni- 
cus's book, and of the opinion maintained in it of the 
motion of the earth, which I at that time believed ; un- 
til it pleased those gentlemen to suspend the book, and 
to declare the opinion false and repugnant to the Holy 
Scriptures. Now, as I know how well it becomes me 
to obey and believe the decisions of my superiors, which 
proceed out of more profound knowledge than the 


weakness of my intellect can attain to, this theory, 
which I send you, which is founded on the motion of 
the earth, I now look upon as a fiction and a dream, 
and beg your Highness to receive it as such. But, as 
poets often learn to prize the creations of their fancy, 
so, in like manner, do I set some value on this absurdi- 
ty of mine. It is true, that when I sketched this little 
work, I did hope that Copernicus would not, after eigh- 
ty years, be convicted of error ; and I had intended to 
develope atad amplify it further ; but a voice from heav- 
en suddenly awakened me, and at once annihilated all 
my confused and entangled fancies." 

It is difficult, however, sometimes to decide wheth- 
er the language of Galileo is ironical, or whether he 
uses it with subtlety, with the hope of evading the 
anathemas of the Inquisition. Thus he ends one of his 
writings with the following passage : "In conclusion, 
since the motion attributed to the earth, which I, as a 
pious and Catholic person, consider most false, and not 
to exist, accommodates itself so well to explain so many 
and such different phenomena, I shall not feel sure that, 
false as it is, it may not just as deludingly correspond 
with the phenomena of comets." 

In the year 1624, soon after the accession of Ur- 
ban the Eighth to the Pontifical chair, Galileo went to 
Rome again, to offer his congratulations to the new 
Pope, as well as to propitiate his favor. He seems to 
have been received with unexpected cordiality ; and, on 
his departure, the Pope commended him to the good 
graces of Ferdinand, Grand Duke of Tuscany, in the 
following terms : " We find in him not only literary 
distinction, but also the love of piety, and he is strong 
in those qualities by which Pontifical good-will is easily 
obtained. And now, when he has been brought to this 
city, to congratulate Us on Our elevation, We have lov- 
ingly embraced him ; nor can We suffer him to return 
to the country whither your liberality recalls him, with- 
out an ample provision of Pontifical love. And that you 
may know how dear he is to Us, we have willed to give 


him this honorable testimonial of virtue and piety. 
And We further signify, that every benefit which you 
shall confer upon him will conduce to Our gratification." 

In the year 1630, Galileo finished a great work, on 
which he had been long engaged, entitled, ' The Dia- 
logue on the Ptolemaic and Copernican Systems/ 
From the notion which prevailed, that he still counte- 
nanced the Copernican doctrine of the earth's motion, 
which had been condemned as heretical, it was some 
time before he could obtain permission from the Inquis- 
itors (whose license was necessary to every book) to 
publish it. This he was able to do, only by employing 
again that duplicity or artifice which would throw dust 
in the eyes of the vain and superstitious priesthood. 
In 1632, the work appeared under the following title : 
' A Dialogue, by Galileo Galilei, Extraordinary Mathe- 
matician of the University of Pisa, and Principal Phi- 
losopher and Mathematician of the Most Serene Grand 
Duke of Tuscany ; in which, in a Conversation of four 
days, are discussed the two principal Systems of the 
World, the Ptolemaic and Copernican, indeterminately 
proposing the Philosophical Arguments as well on one 
side as on the other.' The subtle disguise which he 
wore, may be seen from the following extract from his 
' Introduction,' addressed ' To the discreet Reader.' 

" Some years ago, a salutary edict was promulgated 
at Rome, which, in order to obviate the perilous scan- 
dals of the present age, enjoined an opportune silence 
on the Pythagorean opinion of the earth's motion. 
Some were not wanting, who rashly asserted that this 
decree originated, not in a judicious examination, but 
in ill-informed passion; and complaints were heard, 
that counsellors totally inexperienced in astronomical 
observations ought not, by hasty prohibitions, to clip 
the wings of speculative minds. My zeal could not 
keep silence when I heard these rash lamentations, and 
I thought it proper, as being fully informed with regard 
to that most prudent determination, to appear publicly 
on the theatre of the world, as a witness of the actual 


truth. I happened at that time to be in Rome : I was 
admitted to the audiences, and enjoyed the approbation, 
of the most eminent prelates of that court ; nor did the 
publication of that decree occur without my receiving 
some prior intimation of it. Wherefore, it is my inten- 
tion, in this present work, to show to foreign nations, 
that as much is known of this matter in Italy, and 
particularly in Rome, as ultramontane diligence can 
ever have formed any notion of, and collecting together 
all my own speculations on the Copernican system, to 
give them to understand that the knowledge of all these 
preceded the Roman censures ; and that from this 
country proceed not only dogmas for the salvation of 
the soul, but also ingenious discoveries for the gratifi- 
cation of the understanding. With this object, I have 
taken up in the ' Dialogue' the Copernican side of the 
question, treating it as a pure mathematical hypothesis ; 
and endeavoring, in every artificial manner, to repre- 
sent it as having the advantage, not over the opinion 
of the stability of the earth absolutely, but according to 
the manner in which that opinion is defended by some, 
who indeed profess to be Aristotelians, but .retain only 
the name, and are contented, without improvement, to 
worship shadows, not philosophizing with their own 
reason, but only from the recollection of the four prin- 
ciples imperfectly understood." 

Although the Pope himself, as well as the Inquisitors, 
had examined Galileo's manuscript, and, not having the 
sagacity to detect the real motives of the author, had 
consented to its publication, yet, when the book was 
out, the enemies of Galileo found means to alarm the 
court of Rome, and Galileo was summoned to appear 
before the Inquisition. The philosopher was then sev- 
enty years old, and very infirm, and it was with great 
difficulty that he performed the journey. His unequal- 
led dignity and celebrity, however, commanded the in- 
voluntary respect of the tribunal before which he was 
summoned, which they manifested by permitting him 
to reside at the palace of his friend, the Tuscan Am- 
23 L. A. 


bassador ; and when it became necessary, in the course 
of the inquiry, to examine him in person, although his 
removal to the Holy Office was then insisted upon, yet 
he was not, like other heretics, committed to close and 
solitary confinement. On the contrary, he was lodged 
in the apartments of the Head of the Inquisition, where 
he was allowed the attendance of his own servant, who 
was also permitted to sleep in an adjoining room, and 
to come and go at pleasure. These were deemed ex- 
traordinary indulgences in an age when the punishment 
of heretics usually began before their trial. 

About four months after Galileo's arrival in Rome, 
he was summoned to the Holy Office. He was detain- 
ed there during the whole of that day ; and on the 
next day was conducted, in a penitential dress, to the 
Convent of Minerva, where the Cardinals and Prelates, 
his judges, were assembled for the purpose of passing 
judgement upon him, by which this venerable old man 
was solemnly called upon to renounce and abjure, as 
impious and heretical, the opinions which his whole ex- 
istence had been consecrated to form and strengthen. 
Probably there is not a more curious document in the 
history of science, than that which contains the sen- 
tence of the Inquisition on Galileo, and his consequent 
abjuration. It teaches us so much, both of the dark- 
ness and bigotry of the terrible Inquisition, and of the 
sufferings encountered by those early martyrs of sci- 
ence, that I will transcribe for your perusal, from the 
excellent 'Life of Galileo' in the 'Library of Useful 
Knowledge,' (from which I have borrowed much alrea- 
dy,) the entire record of this transaction. The sen- 
tence of the Inquisition is as follows : 

" We, the undersigned, by the grace of God, Cardi- 
nals of the Holy Roman Church, Inquisitors General 
throughout the whole Christian Republic, Special Depu- 
ties of the Holy Apostolical Chair against heretical de- 
pravity : 

" Whereas, you, Galileo, son of the late Vincenzo 
Galilei of Florence, aged seventy years, were denoun- 

<3ALILEO. 267 

ced in 1615, to this Holy Office, for holding as true a 
false doctrine taught by many, namely, that the sun is 
immovable in the centre of the world, and that the 
earth moves, and also with a diurnal motion ; also, for 
having pupils which you instructed in the same opin- 
ions; also, for maintaining a correspondence on the 
same with some German mathematicians ; also, for 
publishing certain letters on the solar spots, in which 
you developed the same doctrine as true ; also, for an- 
swering the objections which were continually produced 
from the Holy Scriptures, by glozing the said Scriptures, 
according to your own meaning ; and whereas, thereupon 
was produced the copy of a writing, in form of a letter, 
professedly written by you to a person formerly your 
pupil, in which, following the hypothesis of Copernicus, 
you include several propositions contrary to the true 
sense and authority of the Holy Scriptures : therefore, 
this Holy Tribunal, being desirous of providing against 
the disorder and mischief which was thence proceeding 
and increasing, to the detriment of the holy faith, by 
the desire of His Holiness, and of the Most Eminent 
Lords Cardinals of this supreme and universal Inquisi- 
tion, the two propositions of the stability of the sun, and 
motion of the earth, were qualified by the Theological 
Qualifiers, as follows: 

" 1. The proposition that the sun is in the centre of 
the world, and immovable from its place, is absurd, phi- 
losophically false, and formally heretical ; because it is 
expressly contrary to the Holy Scriptures. 

" 2. The proposition that the earth is not the centre 
of the world, nor immovable, but that it moves, and 
also with a diurnal motion, is also absurd, philosophi- 
cally false, and, theologically considered, equally errone- 
ous in faith. 

" But whereas, being pleased at that time to deal 
mildly with you, it was decreed in the Holy Congrega- 
tion, held before His Holiness on the twenty-fifth day 
of February, 1616, that His Eminence the Lord Cardi- 
nal Bellannine should enjoin you to give up altogether 


the said false doctrine ; if you should refuse, that you 
should be ordered by the Commissary of the Holy Office 
to relinquish it, not to teach it to others, nor to defend 
it, and in default of the acquiescence, that you should 
be imprisoned ; and in execution of this decree, on the 
following day, at the palace, in presence of His Emi- 
nence the said Lord Cardinal Bellarmine, after you had 
been mildly admonished by the said Lord Cardinal, 
you were commanded by the acting Commissary of the 
Holy Office, before a notary and witnesses, to relinquish 
altogether the said false opinion, and in future neither 
to defend nor teach it in any manner, neither verbally 
nor in writing, and upon your promising obedience, you 
were dismissed. 

" And, in order that so pernicious a doctrine might be 
altogether rooted out, nor insinuate itself further to the 
heavy detriment of the Catholic truth, a decree emana- 
ted from the Holy Congregation of the Index, prohibit- 
ing the books which treat of this doctrine ; and it was 
declared false, and altogether contrary to the Holy and 
Divine Scripture. 

" And whereas, a book has since appeared, published 
at Florence last year, the title of which showed that you 
were the author, which title is, ' The Dialogue of Gali- 
leo Galilei, on the two principal Systems of the World, 
the Ptolemaic and Copernican ;' and whereas, the Holy 
Congregation has heard that, in consequence of printing 
the said book, the false opinion of the earth's motion 
and stability of the sun is daily gaining ground ; the 
said book has been taken into careful consideration, 
and in it has been detected a glaring violation of the 
said order, which had been intimated to you ; inasmuch 
as in this book you have defended the said opinion, al- 
ready, and in your presence, condemned ; although in 
the said book you labor, with many circumlocutions, to 
induce the belief that it is left by you undecided, and in 
express terms probable ; which is equally a very grave 
error, since an opinion can in no way be probable which 
has been already declared and finally determined con- 


trary to the Divine Scripture. Therefore, by Our order, 
you have been cited to this Holy Office, where, on your 
examination upon oath, you have acknowledged the said 
book as written and printed by you. You also confessed 
that you began to write the said book ten or twelve 
years ago, after the order aforesaid had been given. 
Also, that you demanded license to publish it, but with- 
out signifying to those who granted you this permission, 
that you had been commanded not to hold, defend, or 
teach, the said doctrine in any manner. You also con- 
fessed, that the style of said book was, in many places, 
so composed, that the reader might think the arguments 
adduced on the false-side to be so worded, as more effec- 
tually to entangle the understanding than to be easily 
solved, alleging, in excuse, that you have thus run into 
an error, foreign (as you say) to your intention, from 
writing in the form of a dialogue, and in consequence 
of the natural complacency which every one feels with 
regard to his own subtilties, and in showing himself 
more skilful than the generality of mankind in contriv- 
ing, even in favor of false propositions, ingenious and 
apparently probable arguments. 

" And, upon a convenient time being given you for 
making your defence, you produced a certificate in 
the handwriting of His Eminence, the Lord Cardinal 
Bellarmine, procured, as you said, by yourself, that you 
might defend yourself against the calumnies of your ene- 
mies, who reported that you had abjured your opinions, 
and had been punished by the Holy Office ; in which 
certificate it is declared, that you had not abjured, nor 
had been punished, but merely that the declaration made 
by his Holiness, and promulgated by the Holy Congre- 
gation of the Index, had been announced to you, which 
declares that the opinion of the motion of the earth, and 
stability of the sun, is contrary to the Holy Scriptures, 
and therefore cannot be held or defended. Wherefore, 
since no mention is there made of two articles of the 
order, to wit, the order * not to teach,' and ' in any man- 
ner,' you argued that we ought to believe that, in the 


lapse of fourteen or sixteen years, they had escaped 
your memory, and that this was also the reason why 
you were silent as to the order, when you sought per- 
mission to publish your book, and that this is said by 
you, not to excuse your error, but that it may be attrib- 
uted to vain-glorious ambition rather than to malice. 
But this very certificate, produced on your behalf, has 
greatly aggravated your offence, since it is therein de- 
clared, that the said opinion is contrary to the Holy 
Scriptures, and yet you have dared to treat of it, and to 
argue that it is probable ; nor is there any extenuation 
in the license artfully and cunningly extorted by you, 
since you did not intimate the command imposed upon 
y,ou. But whereas, it appeared to Us that you had not 
disclosed the whole truth with regard to your intentions, 
We thought it necessary to proceed to the rigorous ex- 
amination of you, in which (without any prejudice to 
what you had confessed, and which is above detailed 
against you, with regard to your said intention) you an- 
swered like a good Catholic. 

"Therefore, having seen and maturely considered 
the merits of your cause, with your said confessions 
and excuses, and every thing else which ought to be 
seen and considered, We have come to the underwrit- 
ten final sentence against you : 

" Invoking, therefore, the most holy name of our 
Lord Jesus Christ, and of his Most Glorious Virgin 
Mother, Mary, by this Our final sentence, which, sitting 
in council and judgement for the tribunal of the Rever- 
end Masters of Sacred Theology, and Doctors of both 
Laws, Our Assessors, We put forth in this writing 
touching the matters and controversies before Us, be- 
tween the Magnificent Charles Sincerus, Doctor of both 
Laws, Fiscal Proctor of this Holy Office, of the one part, 
and you, Galileo Galilei, an examined and confessed 
criminal from this present writing now in progress, as 
above, of the other part, We pronounce, judge, and 
declare, that you, the said Galileo, by reason of these 
things which have been detailed in the course of this 


writing, and which, as above, you have confessed, have 
rendered yourself vehemently suspected, by this Holy 
Office, of heresy ; that is to say, that you believe and 
hold the false doctrine, and contrary to the Holy and 
Divine Scriptures, namely, that the sun is the centre of 
the world, and that it does not move from east to west, 
and that the earth does move, and is not the centre of 
the world ; also, that an opinion can be held and sup- 
ported, as probable, after it has been declared and final- 
ly decreed contrary to the Holy Scripture, and conse- 
quently, that you have incurred all the censures and 
penalties enjoined and promulgated in the sacred can- 
ons, and other general and particular constitutions 
against delinquents of this description. From which it 
is Our pleasure that you be absolved, provided that, 
with a sincere heart and unfeigned faith, in Our pres- 
ence, you abjure, curse, and detest, the said errors and 
heresies, and every other error and heresy, contrary to 
the Catholic and Apostolic Church of Rome, in the 
form now shown to you. 

" But that your grievous and pernicious error and 
transgression may not go altogether unpunished, and 
that you may be made more cautious in future, and 
may be a warning to others to abstain from delinquen- 
cies of this sort, We decree, that the book of the Dia- 
logues of Galileo Galilei be prohibited by a public edict, 
and We condemn you to the formal prison of this Holy 
Office for a period determinable at Our pleasure ; and, 
by way of salutary penance, We order you, during the 
next three years, to recite, once a week, the seven peni- 
tential psalms, reserving to Ourselves the power of mod- 
erating, commuting, or taking off the whole or part of 
the said punishment, or penance. 

" And so We say, pronounce, and by Our sentence 
declare, decree, and reserve, in this and in every other 
better form and manner, which lawfully We may and 
can use. So We, the subscribing Cardinals, pro- 
nounce." [Subscribed by seven Cardinals.] 

In conformity with the foregoing sentence, Galileo 


was made to kneel before the Inquisition, and make the 
following Abjuration : 

" I, Galileo Galilei, son of the late Vincenzo Galilei, 
of Florence, aged seventy years, being brought person- 
ally to judgement, and kneeling before you, Most Emi- 
nent and Most Reverend Lords Cardinals, General In- 
quisitors of the Universal Christian Republic against 
heretical depravity, having before my eyes the Holy 
Gospels, which I touch with my own hands, swear, that 
I have always believed, and with the help of God will 
in future believe, every article which the Holy Catho- 
lic and Apostolic Church of Rome holds, teaches, and 
preaches. But because I had been enjoined, by this 
Holy Office, altogether to abandon the false opinion 
which maintains that the sun is the centre and immov- 
able, and forbidden to hold, defend, or teach, the said 
false doctrine, in any manner ; and after it had been 
signified to me that the said doctrine is repugnant to 
the Holy Scripture, I have written and printed a book, 
in which I treat of the same doctrine now condemned, 
and adduce reasons with great force in support of the 
same, without giving any solution, and therefore have 
been judged grievously suspected of heresy ; that is to 
say, that I held and believed that the sun is the centre 
of the world and immovable, and that the earth is not 
the centre and movable ; willing, therefore, to remove 
from the minds of Your Eminences, and of every Cath- 
olic Christian, this vehement suspicion rightfully enter- 
tained towards me, with a sincere heart and unfeigned 
faith, I abjure, curse, and detest, the said errors and 
heresies, and generally every other error and sect con- 
trary to the said Holy Church ; and I swear, that I will 
never more in future say or assert any thing, verbally or 
in writing, which may give rise to a similar suspicion of 
me : but if I shall know any heretic, or any one sus- 
pected of heresy, that I will denounce him to this Holy 
Office, or to the Inquisitor and Ordinary of the place 
in which I may be. I swear, moreover, and promise, 
that I will fulfil and observe fully, all the penances 


which have been or shall be laid on me by this Holy 
Office. But if it shall happen that I violate any of 
my said promises, oaths, and protestations, (which God 
avert !) I subject myself to all the pains and punish- 
ments which have been decreed and promulgated by 
the sacred canons, and other general and particular 
constitutions, against delinquents of this description. 
So may God help me, and his Holy Gospels, which I 
touch with my own hands. I, the above-named Galileo 
Galilei, have abjured, sworn, promised, and bound my- 
self, as above ; and in witness thereof, with my own 
hand have subscribed this present writing of my abjura- 
tion, which I have recited, word for word. 

" At Rome, in the Convent of Minerva, twenty-sec- 
ond June, 1633, I, Galileo Galilei, have abjured as 
above, with my own hand." 

From the court Galileo was conducted to prison, to be 
immured for life in one of the dungeons of the Inquisi- 
tion. His sentence was afterwards mitigated, and he 
was permitted to return to Florence ; but the humilia- 
tion to which he had been subjected pressed heavily on 
his spirits, beset as he was with infirmities, and totally 
blind, and he never more talked or wrote on the subject 
of astronomy. 

There was enough in the character of Galileo to com- 
mand a high admiration. There was much, also, in his 
sufferings in the cause of science, to excite the deepest 
sympathy, and even compassion. He is moreover uni- 
versally represented to have been a man of great equa- 
nimity, and of a noble and generous disposition. No sci- 
entific character of the age, or perhaps of any age, forms 
a structure of finer proportions, or wears in a higher de- 
gree the grace of symmetry. Still, we cannot approve 
of his employing artifice in the promulgation of truth; 
and we are compelled to lament that his lofty spirit bow- 
ed in the final conflict. How far, therefore, he sinks be- 
low the dignity of the Christian martyr ! " At the age 
of seventy," says Dr. Brewster, in his life of Sir Isaac 
Newton, " on his bended knees, and with his right 


hand resting on the Holy Evangelists, did this patriarch 
of science avow his present and past belief in the dog- 
mas of the Romish Church, abandon as false and heret- 
ical the doctrine of the earth's motion and of the sun's 
immobility, and pledge himself to denounce to the In- 
quisition any other person who was even suspected of 
heresy. He abjured, cursed, and detested, those eter- 
nal and immutable truths which the Almighty had per- 
mitted him to be the first to establish. Had Galileo but 
added the courage of the martyr to the wisdom of the 
sage ; had he carried the glance of his indignant eye 
round the circle of his judges ; had he lifted his hands 
to heaven, and called the living God to witness the truth 
and immutability of his opinions ; the bigotry of his 
enemies would have been disarmed, and science would 
have enjoyed a memorable triumph." 



" Into the Heaven of Heavens I have presumed, 
An earthly guest, and drawn empyreal air." Milton. 

THE consideration of the system of Jupiter and his 
satellites led us to review the interesting history of Gal- 
ileo, who first, by means of the telescope, disclosed the 
knowledge of that system to the world. I will now 
proceed with the other superior planets. 

SATURN, as well as Jupiter, has within itself a system 
on a scale of great magnificence. In size it is next to 
Jupiter the largest of the planets, being seventy-nine 
thousand miles in diameter, or about one thousand 
times as large as the earth. It has likewise belts on its 
surface, and is attended by seven satellites. But a still 
more wonderful appendage is its Ring, a broad wheel, 
encompassing the planet at a great distance from it. 
As Saturn is nine hundred millions of miles from us, 
we require a more powerful telescope to see his glories, 

SATURN. 275 

in all their magnificence, than we do to enjoy a full 
view of the system of Jupiter. When we are privi- 
leged with a view of Saturn, in his most favorable po- 
sitions, through a telescope of the larger class, the. 
mechanism appears more wpnderful than even that of 

Saturn's ring, when viewed with telescopes of a high 
power, is found to consist of two concentred rings, 
separated from each other by a dark space. Although 
this division of the rings appears to us, on account of 
our immense distance, as only a fine line, yet it is, in 
reality, an interval of not less than eighteen hundred 
miles. The dimensions of the whole system are, in 
round numbers, as follows : 


Diameter of the planet, . . . . . 79,000 
From the surface of the planet to the inner ring, 20,000 
Breadth of the inner ring, . . . 17,000 
Interval between the rings, .... 1,800 
Breadth of the outer ring, . * .; . 10,500 
Extreme dimensions from outside to outside, 176,000 

Figure 60, facing page 247, represents Saturn, as it 
appears to a powerful telescope, surrounded by its rings, 
and having its body striped with dark belts, somewhat 
similar, but broader and less strongly marked than those 
of Jupiter. In telescopes of inferior power, but still 
sufficient to see the ring distinctly, we should scarcely 
discern the belts at all. We might, however, observe 
the shadow cast upon the ring by the planet, (as seen 
in the figure on the right, on the upper side ;) and, in 
favorable situations of the planet, we might discern 
glimpses of the shadow of the ring on the body of the 
planet, on the lower side beneath the ring. To see 
the division of the ring and the satellites requires a 
better telescope than is in possession of most observers. 
With smaller telescopes, we may discover an oval fig- 
ure of peculiar appearance, which it would be difficult 
to interpret. Galileo, who first saw it in the year 1610, 


recognised this peculiarity, but did not know what it 
meant. Seeing something in the centre with two pro- 
jecting arms, one on each side, he concluded that the 
planet was triple-shaped. This was, at the time, all he 
could learn respecting it, as the telescopes he possessed 
were very humble, compared with those now used by 
astronomers. The first constructed by him magnified 
but three times ; his second, eight times ; and his best, 
only thirty times, which is no better than a common 

It was the practice of the astronomers of those days 
to give the first intimation of a new discovery in a Lat- 
in verse, the letters of which were transposed. This 
would enable them to claim priority, in case any other 
person should contest the honor of the discovery, and 
at the same time would afford opportunity to complete 
their observations, before they published a full account 
of them. Accordingly, Galileo announced the discov- 
ery of the singular appearance of Saturn under this 
disguise, in a line which, when the transposed letters 
were restored to their proper places, signified that he 
had observed, " that the most distant planet is triple- 
formed."* He shortly afterwards, at the request of his 
patron, the Emperor Rodolph, gave the solution, and 
added, " I have, with great admiration, observed that 
Saturn is not a single star, but three together, which, 
as it were, touch each other ; they have no relative mo- 
tion, and are constituted of this form, oOo, the middle 
one being somewhat larger than the two lateral ones. 
If we examine them with an eye-glass which magnifies 
the surface less than one thousand times, the three stars 
do not appear very distinctly, but Saturn has an oblong 
appearance, like that of an olive, thus, o. Now, I 
have discovered a court for Jupiter, (alluding to his 
satellites,) and two servants for this old man, (Saturn,) 
who aid his steps, and never quit his side." 

It was by this mystic light that Galileo groped his 

* Altissimum planetam tergeminum observavi. Or, as transposed, 
Smaismrmilme poeta leumi bvne nugttaviras. 

SATURN. 277 

way through an organization which, under the more 
powerful glasses of his successors, was to expand into 
a mighty orb, encompassed by splendid rings of vast 
dimensions, the whole attended by seven bright satel- 
lites. This system was first fully developed by Huy- 
ghens, a Dutch astronomer, about forty years after- 
wards.* It requires a superior telescope to see it to 
advantage ; but, when seen through such a telescope, 
it is one of the most charming spectacles afforded to 
that instrument. To give some idea of the properties 
of a telescope suited to such observations, I annex an 
extract from an account, that was published a few years 
since, of a telescope constructed by Mr. Tully, a distin- 
guished English artist. " The length of the instrument 
was twelve feet, but was easily adjusted, and was per- 
fectly steady. The magnifying powers ranged from 
two hundred to seven hundred and eighty times ; but 
the great excellence of the telescope consisted more in 
the superior distinctness and brilliancy with which ob- 
jects were seen through it, than in its magnifying pow- 
ers. With a power of two hundred and forty, the 
light of Jupiter was almost more than the eye could 
bear, and his satellites appeared as bright as Sirius, 
but with a clear and steady light ; and the belts and 
spots on the face of the planet were most distinctly 
defined. With a power of nearly four hundred, Sa- 
turn appeared large and well defined, and was one of 
the most beautiful objects that can well be conceived." 
That the ring is a solid opaque substance, is shown 
by its throwing its shadow on the body of the planet 
on the side nearest the sun, and on the other side re- 
ceiving that of the body. The ring encompasses the 
equatorial regions of the planet, and the planet revolves 
on an axis which is perpendicular to the plane of the 

* In imitation of Galileo, Huyghens announced his discovery in 
this form raaaaaaacccccdeeeeeghiiiiiiillllmmnn 
nnnnnnnooooppqrrstttttuuuuu; which he afterwards 
recomposed into this sentence : JLnnulo cingitur, tenui, piano, nus- 
quam coh&re?iie, ad eclipticam inclinato. 

24 L. A. 


ring in about ten and a half hours. This is known by 
observing the rotation of certain dusky spots, which 
sometimes appear on its surface. This motion is near- 
ly the same with the diurnal motion of Jupiter, subject- 
ing places on the equator of the planet to a very swift 
revolution, and occasioning a high degree of compres- 
sion at the poles, the equatorial being to the polar di- 
ameter in the high ratio of eleven to ten. 

Saturn's ring, in its revolution around the sun, always 
remains parallel to itself. If we hold opposite to the 
eye a circular ring or disk, like a piece of coin, it will 
appear as a complete circle only when it is at right an- 
gles to the axis of vision. When it is oblique to that 
axis, it will be projected into an ellipse more and more 
flattened, as its obliquity is increased, until, when its 
plane coincides with the axis of vision, it is projected 
into a straight line. Please to take some circle, as a 
flat plate, (whose rim may well represent the ring of 
Saturn.) and hold it in these different positions before 
the eye. Now, place on the table a lamp to represent 
the sun, and holding the ring at a certain distance, in- 
clined a little towards the lamp, carry it round the 
lamp, always keeping it parallel to itself. During its 
revolution, it will twice present its edge to the lamp at 
opposite points ; and twice, at places ninety degrees 
distant from those points, it will present its broadest 
face towards the lamp. At intermediate points, it will 
exhibit an ellipse more or less open, according as it is 
nearer one or the other of the preceding positions. It 
will be seen, also, that in one half of the revolution, 
the lamp shines on one side of the ring, and in the 
other half of the revolution, on the other side. 

Such would be the successive appearances of Sa- 
turn's ring to a spectator on the sun ; and since the earth 
is, in respect to so distant a body as Saturn, very near 
the sun, these appearances are presented to us nearly 
in the same manner as though we viewed them from 
the sun. Accordingly, we sometimes see Saturn's ring 
under the form of a broad ellipse, which grows contin- 

SA.TURN. 279 

ually more and more acute, until it passes into a line, 
and we either lose sight of it, altogether, or, by the aid 
of the most powerful telescopes, we see it as a fine 
thread of light drawn across the disk, and projecting 
out from it on each side. As the whole revolution oc- 
cupies thirty years, and the edge is presented to the 
sun twice in the revolution, this last phenomenon, 
namely, the disappearance of the ring, takes place every 
fifteen years. 

You may perhaps gain a still clearer idea of the fore- 
going appearances from the following diagram, Fig. 61. 

Fig. 61. 

Let A, B, C, &c., represent successive positions of Sa- 
turn and his ring, in different parts of his orbit, while 
a b represents the orbit of the earth. Please to re- 
mark, that these orbits are drawn so elliptical, not to 
represent the eccentricity of either the earth's or Sa- 
turn's orbit, but merely as the projection of circles seen 
very obliquely. Also, imagine one half of the body of 
the planet and of the ring to be above the plane of the 
paper, and the other half below it. Were the ring, 
when at C and G, perpendicular to C G, it would be 
seen by a spectator situated at a or b as a perfect cir- 
cle ; but being inclined to the line of vision twenty- 
eight degrees four minutes, it is projected into an ellipse. 
This ellipse contracts in breadth as the ring passes 
towards its nodes at A and E, where it dwindles into 
a straight line. From E to G the ring opens again, 


becomes broadest at G, and again contracts, till it be- 
comes a straight line at A, and from this point expands, 
till it recovers its original breadth at C. These succes- 
sive appearances are all exhibited to a telescope of 
moderate powers. 

The ring is extremely thin, since the smallest satel- 
lite, when projected on it, more than covers it. The 
thickness is estimated at only one hundred miles. Sa- 
turn's ring shines wholly by reflected light derived from 
the sun. This is evident from the fact that that side 
only which is turned towards the sun is enlightened ; 
and it is remarkable, that the illumination of the ring 
is greater than that of the planet itself, but the outer 
ring is less bright than the inner. Although we view 
Saturn's ring nearly as though we saw it from the sun, 
yet the plane of the ring produced may pass between 
the earth and the sun, in which case, also, the ring be- 
comes invisible, the illuminated side being wholly turned 
from us. Thus, when the ring is approaching its node 
at E, a spectator at a would have the dark side of the 
ring presented to him. The ring was invisible in 1833, 
and will be invisible again in 1847. The northern side 
of the ring will be in sight until 1855, when the south- 
ern side will come into view. It appears, therefore, 
that there are three causes for the disappearance of 
Saturn's ring : first, when the edge of the ring is pre- 
sented to the sun ; secondly, when -the edge is present- 
ed to the earth ; and thirdly, when the unilluminated 
side is towards the earth. 

Saturn's ring revolves in its own plane in about ten 
ind a half hours. La Place inferred this from the doc- 
trine of universal gravitation. He proved that such a 
rotation was necessary ; otherwise, the matter of which 
the ring is composed would be precipitated upon its 
primary. He showed that, in order to sustain itself, its 
period of rotation must be equal to the time of revolu- 
tion of a satellite, circulating around Saturn at a dis- 
tance from it equal to that of the middle of the ring, 
which period would be about ten and a half hours. By 

SATURN. 281 

means of spots in the ring, Dr. Herschel followed the 
ring in its rotation, and actually found its period to be 
the same as assigned by La Place, a coincidence 
which beautifully exemplifies the harmony of truth. 

Although the rings have very nearly the same centre 
with the planet itself, yet recent measurements of ex- 
treme delicacy have demonstrated, that the coincidence 
is not mathematically exact, but that the centre of 
gravity of the rings describes around that of the body 
a very minute orbit. " This fact," says Sir J. Her- 
schel, " unimportant as it may seem, is of the utmost 
consequence to the stability of the system of rings. 
Supposing them mathematically perfect in their circular 
form, and exactly concentric with the planet, it is de- 
monstrable that they would form (in spite of their cen- 
trifugal force) a system in a state of unstable equilib- 
rium, which the slightest external power would subvert, 
not by causing a rupture in the substance of the rings, 
but by precipitating them unbroken upon the surface 
of the planet." The ring may be supposed of an un- 
equal breadth in its different parts, and as consisting 
of irregular solids, whose common centre of gravity 
does not coincide with the centre of the figure. Were 
it not for this distribution of matter, its equilibrium 
would be destroyed by the slightest force, such as the 
attraction of a satellite, and the ring would finally pre- 
cipitate itself upon the planet. Sir J. Herschel further 
observes, that, u as the smallest difference of velocity 
between the planet and its rings must infallibly precip- 
itate the rings upon the planet, never more to separate, 
it follows, either that their motions in their common 
orbit round the sun must have been adjusted to each 
other by an external power, with the minutest precision, 
or that the rings must have been formed about the 
planet while subject to their common orbitual motion, 
and under the full and free influence of all the acting 

"The rings of Saturn must present a magnificent 
spectacle from those regions of the planet which lie on 


their enlightened sides, appearing as vast arches span- 
ning the sky from horizon to horizon, and holding an 
invariable situation among the stars. On the other 
hand, in the region beneath the dark side, a solar 
eclipse of fifteen years in duration, under their shadow, 
must afford (to our ideas) an inhospitable abode to an- 
imated beings, but ill compensated by the full light of 
its satellites. But we shall do wrong to judge of the 
fitness or unfitness of their condition, from what we 
see around us, when, perhaps, the very combinations 
which convey to our minds only images of horror, may 
be in reality theatres of the most striking and glorious 
displays of beneficent contrivance." 

Saturn is attended by seven satellites. Although 
they are bodies of considerable size, their great distance 
prevents their being visible to any telescope but such 
as afford a strong light and high magnifying powers. 
The outermost satellite is distant from the planet more 
than thirty times the planet's diameter, and is by far 
the largest of the whole. It exhibits, like the satellites 
of Jupiter, periodic variations of light, which prove its 
revolution on its axis in the time of a sidereal revolu- 
tion about Saturn, as is the case with our moon, while 
performing its circuit about the earth. The next sat- 
ellite in order, proceeding inwards, is tolerably con- 
spicuous ; the three next are very minute, and require 
powerful telescopes to see them ; while the two interior 
satellites, which just skirt the edge of the ring, and 
move exactly in its plane, have never been discovered 
but with the most powerful telescopes which human 
art has yet constructed, and then only under peculiar 
circumstances. At the time of the disappearance of 
the rings, (to ordinary telescopes.) they were seen by 
Sir William Herschel, with his great telescope, pro- 
jected along the edge of the ring, and threading, like 
beads, the thin fibre of light to which the ring is then 
reduced. Owing to the obliquity of the ring, and of 
the orbits of the satellites, to that of their primary, 
there are no eclipses of the satellites, the two interior 

URANUS. 283 

ones excepted, until near the time when the ring is 
seen edgewise. 

" The firmament of Saturn will unquestionably pre- 
sent to view a more magnificent and diversified scene 
of celestial phenomena than that of any other planet 
in our system. It is placed nearly in the middle of 
that space which intervenes between the sun and the 
orbit of the remotest planet. Including its rings and 
satellites, it may be considered as the largest body or 
system of bodies within the limits of the solar system ; 
and it excels them all in the sublime and diversified 
apparatus with which it is accompanied. In these re- 
spects, Saturn may justly be considered as the sove- 
reign among the planetary hosts. The prominent parts 
of its celestial scenery may be considered as belonging 
to its own system of rings and satellites, and the views 
which will occasionally be opened of the firmament of 
the fixed stars ; for few of the other planets will make 
their appearance in its sky. Jupiter will appear alter- 
nately as a morning and an evening star, with about the 
same degree of brilliancy it exhibits to us ; but it will 
seldom be conspicuous, except near the period of its 
greatest elongation ; and it will never appear to remove 
from the sun further than thirty-seven degrees, and con- 
sequently will not appear so conspicuous, nor for such 
a length of time, as Venus does to us. Uranus is the 
only other planet which will be seen from Saturn, and 
it will there be distinctly perceptible, like a star of the 
third magnitude, when near the time of its opposition 
to the sun. But near the time of its conjunction it 
will be completely invisible, being then eighteen hun- 
dred millions of miles more distant than at the opposi- 
tion, and eight hundred millions of miles more distant 
from Saturn than it ever is from the earth at any pe- 

URANUS. Uranus is the remotest planet belonging 
to our system, and is rarely visible, except to the tele- 
scope. Although his diameter is more than four times 
* Dick's Celestial Scenery.* 


that of the earth, being thirty-five thousand one hun- 
dred and twelve miles, yet his distance from the sun is 
likewise nineteen times as great as the earth's distance, 
or about eighteen hundred millions of miles. His 
revolution around the sun occupies nearly eighty-four 
years, so that his position in the heavens, for several 
years in succession, is nearly stationary. His path lies 
very nearly in the ecliptic, being inclined to it less than 
one degree. The sun himself, when seen from Uranus 
dwindles almost to a star, subtending, as it does, an 
angle of only one degree and forty minutes ; so that 
the surface of the sun would appear there four hundred 
times less than it it does to us. This planet was dis- 
covered by Sir William Herschel on the thirteenth of 
March, 1781. His attention was attracted to it by the 
largeness of its disk in the telescope ; and finding that 
it shifted its place among the stars, he at first took it for 
a comet, but soon perceived that its orbit was not eccen- 
tric, like the orbits of comets, but nearly circular, like 
those of the planets. It was then recognised as a new 
member of the planetary system, a conclusion which 
has been justified by all succeeding observations. It 
was named by the discoverer the George Star, (Geor- 
gium Sidus,) after his munificent patron, George the 
Third ; in the United States, and in some other coun- 
tries, it was called Herschel ; but the name Uranus, 
from a Greek word, (OVQUVOC, Ouranos,} signifying the 
oldest of the gods, has finally prevailed. So distant is 
Uranus from the sun, that light itself, which moves 
nearly twelve millions of miles every minute, would re- 
quire more than two hours and a half to pass to it from 
the sun. 

And now, having contemplated all the planets sep- 
arately, just cast your eyes on the diagram facing page 
236, Fig. 53, and you will see a comparative view of 
the various magnitudes of the sun, as seen from each 
of the planets. 

Uranus is attended by six satellites. So minute 
objects are they, that they can be seen only by power- 

URANUS. 285 

ful telescopes. Indeed, the existence of more than two 
is still considered as somewhat doubtful. These two, 
however, offer remarkable and indeed quite unexpect- 
ed and unexampled peculiarities. Contrary to the 
unbroken analogy of the whole planetary system, the 
planes of their orbits are nearly perpendicular to the 
ecliptic, and in these orbits their motions are retrograde ; 
that is, instead of advancing from west to east around 
their primary, as is the case with all the other planets 
and satellites, they move in the opposite direction. 
With this exception, all the motions of the planets, 
whether around their own axes, or around the sun, are 
from west to east. The sun himself turns on his axis 
from west to east ; all the primary planets revolve 
around the sun from west to east ; their revolutions on 
their own axes are also in the same direction ; all the 
secondaries, with the single exception above mentioned, 
move about their primaries from west to east; and, 
finally, such of the secondaries as have been discovered 
to have a diurnal revolution, follow the same course. 
Such uniformity among so many motions could have 
resulted only from forces impressed upon them by the 
same Omnipotent hand ; and few things in the creation 
more distinctly proclaim that God made the world. 

Retiring now to this furthest verge of the solar sys- 
tem, let us for a moment glance at the aspect of the 
firmament by night. Notwithstanding we have taken 
a flight of eighteen hundred millions of miles, the same 
starry canopy bends over our heads ; Sirius still shines 
with exactly the same splendor as here ; Orion, the 
Scorpion, the Great and the Little Bear, all occupy the 
same stations ; and the Galaxy spans the sky with the 
same soft and mysterious light. The planets, however, 
with the exception of Saturn, are all lost to the view, 
being too near the sun ever to be seen ; and Saturn 
himself is visible only at distant intervals, at periods of 
fifteen years, when at its greatest elongations from the 
sun, and is then too near the sun to permit a clear view 
of his rings, much less of the satellites that unite with 


the rings to compose his gorgeous retinue. Comets, 
moving slowly as they do when so distant from the sun, 
will linger much longer in the firmament of Uranus 
than in ours. 

Although the sun sheds by day a dim and cheerless 
light, yet the six satellites that enlighten and diversify 
the nocturnal sky present interesting aspects. " Let 
us suppose one satellite presenting a surface in the sky 
eight or ten times larger than our moon ; a second, five 
or six times larger ; a third, three times larger ; a fourth, 
twice as large ; a fifth, about the same size as the 
moon ; a sixth, somewhat smaller ; and, perhaps, three 
or four others of different apparent dimensions : let us 
suppose two or three of those, of different phases, 
moving along the concave of the sky, at one period 
four or five of them dispersed through the heavens, one 
rising above the horizon, one setting, one on the merid- 
ian, one towards the north, and another towards the 
south ; at another period, five or six of them displaying 
their lustre in the form of a half moon, or a crescent, 
in one quarter of the heavens ; and, at another time, 
the whole of these moons shining, with full enlightened 
hemispheres, in one glorious assemblage, and we shall 
have a faint idea of the beauty, variety, and sublimity 
of the firmament of Uranus."* 

The New Planets, Ceres, Pallas, Juno, and Vesta. 
The commencement of the present century was ren- 
dered memorable in the annals of astronomy, by the 
discovery of four new planets, occupying the long va- 
cant tract between Mars and Jupiter. Kepler, from 
some analogy which he found to subsist among the dis- 
tances of the planets from the sun, had long before 
suspected the existence of one at this distance ; and 
his conjecture was rendered more probable by the dis- 
covery of Uranus, which follows the analogy of the other 
planets. So strongly, indeed, were astronomers im- 
pressed with the idea that a planet would be found be- 
tween Mars and Jupiter, that, in the hope of discovering 
* Pick's ' Celestial Scenery,' 


it, an association was formed on the continent of Eu- 
rope, of twenty-four observers, who divided the sky 
into as many zones, one of which was allotted to each 
member of the association. The discovery of the first 
of these bodies was, however, made accidentally by 
Piazzi, an astronomer of Palermo, on the first of Janu- 
ary, 1801. It was shortly afterwards lost sight of on 
account of its proximity to the sun, and was not seen 
again until the close of the year, when it was re-dis- 
covered in Germany. Piazzi called it Ceres, in honor 
of the tutelary goddess of Sicily, and her emblem, the 
sickle, (9) has been adopted as its appropriate symbol. 

The difficulty of finding Ceres induced Dr. Olbers, 
of Bremen, to examine with particular care all the small 
stars that lie near her path, as seen from the earth ; and, 
while prosecuting these observations, in March, 1802, 
he discovered another similar body, very nearly at the 
same distance from the sun, and resembling the former 
in many other particulars. The discoverer gave to this 
second planet the name of Pallas, choosing for its sym- 
bol the lance, ($) the characteristic of Minerva. 

The most surprising circumstance connected with 
the discovery of Pallas was the existence of two plan- 
ets at nearly the same distance from the sun, and ap- 
parently crossing the ecliptic in the same part of the 
heavens, or having the same node. On account of this 
singularity, Dr. Olbers was led to conjecture that Ceres 
and Pallas are only fragments of a larger planet, which 
had formerly circulated at the same distance, and been 
shattered by some internal convulsion. The hypothe- 
sis suggested the probability that there might be other 
fragments, whose orbits might be expected to cross 
the ecliptic at a common point, or to have the same 
node. Dr. Olbers, therefore, proposed to examine 
carefully, every month, the two opposite parts of the 
heavens in which the orbits of Ceres and Pallas in- 
tersect one another, with a view to the discovery of 
other planets, which might be sought for in those parts 
with a greater chance of success, than in a wider zone, 


embracing the entire limits of these orbits. According- 
ly, in 1804, near one of the nodes of Ceres and Pallas, 
a third planet was discovered. This was called Juno, 
and the character (<J>) was adopted for its symbol, 
representing the starry sceptre of the Queen of Olym- 
pus. Pursuing the same researches, in 1807 a fourth 
planet was discovered, to which was given the name 
of Vesta, and for its symbol the character (f[) was 
chosen, an altar surmounted with a censer holding 
the sacred fire. 

The average distance of these bodies from the sun 
is two hundred and sixty-one millions of miles ; and it 
is remarkable that their orbits are very near together. 
Taking the distance of the earth from the sun for uni- 
ty, their respective distances are 2.77, 2.77, 2.67, 2.37. 
Their times of revolution around the sun are nearly 
equal, averaging about four and a half years. 

In respect to the inclination of their orbits to the 
ecliptic, there is also considerable diversity. The orbit 
of Vesta is inclined only about seven degrees, while 
that of Pallas is more than thirty-four degrees. They 
all, therefore, have a higher inclination than the orbits 
of the old planets, and of course make excursions from 
the ecliptic beyond the limits of the zodiac. Hence 
they have been called the ultra-zodiacal planets. 
When first discovered, before their place in the system 
was fully ascertained it was also proposed to call them 
asteroids, a name implying that they were planets un- 
der the form of stars. Their title, however, to take 
their rank among the primary planets, is now generally 

The eccentricity of their orbits is also, in general, 
greater than that of the old planets. You will recol- 
lect that this language denotes that their orbits are 
more elliptical, or depart further from the circular form. 
The eccentricities of the orbits of Pallas and Juno ex- 
ceed that of the orbit of Mercury. The asteroids 
differ so much, however, in eccentricity, that their or- 
bits may cross each other. The orbits of the old plan- 


ets are so nearly circular, and at such a great distance 
apart, that there is no danger of their interfering with 
each other. The earth, for example, when at its nearest 
distance from the sun, will never come so near it as 
Venus is when at its greatest distance, and therefore 
can never cross the orbit of Venus. But since the av- 
erage distance of Ceres and Pallas from the sun is about 
the same, while the eccentricity of the orbit of Pallas 
is much greater than that of Ceres, consequently, Pal- 
las may come so near to the sun at its perihelion, as to 
cross the orbit of Ceres. 

The small size of the asteroids constitutes one of 
their most remarkable peculiarities. The difficulty of 
estimating the apparent diameter of bodies at once so 
very small and so far off, would lead us to expect dif- 
ferent results in the actual estimates. Accordingly, 
while Dr. Herschel estimates the diameter of Pallas at 
only eighty miles, Schroeter places it as high as two 
thousand miles, or about the diameter of the moon. 
The volume of Vesta is estimated at only one fifteen 
thousandth part of the earth's, and her surface is only 
about equal to that of the kingdom of Spain. 

These little bodies are surrounded by atmospheres 
of great extent, some of which are uncommonly lumi- 
nous, and others appear to consist of nebulous matter, 
like that of comets. These planets shine with a more 
vivid light than might be expected, from their great dis- 
tance and diminutive size ; but a good telescope is es- 
sential for obtaining a distinct view of their phenomena. 

Although the great chasm which occurs between 
Mars and Jupiter, a chasm of more than three hun- 
dred millions of miles, suggested long ago the idea 
of other planetary bodies occupying that part of the 
solar system, yet the discovery of the asteroids does 
not entirely satisfy expectation since they are bodies 
so dissimilar to the other members of the series in size, 
in appearance, and in the form and inclinations of their 
orbits. Hence, Dr. Olbers, the discoverer of three of 
these bodies, held that they were fragments of a single 

25 L. A. 


large planet, which once occupied that place in the 
system, and which exploded in different directions by 
some internal violence. Of the fragments thus projec- 
ted into space, some would be propelled in such direc- 
tions and with such velocities, as, under the force of 
projection and that of the solar attraction, would make 
them revolve in regular orbits around the sun. Others 
would be so projected among the other bodies in the 
system, as to be thrown in very irregular orbits, appar- 
ently wandering lawless through the skies. The larger 
fragments would receive the least impetus from the ex- 
plosive force, and would therefore circulate in an orbit 
deviating less than any other of the fragments from the 
original path of the large planet ; while the lesser frag- 
ments, being thrown off with greater velocity, would re- 
volve in orbits more eccentric, and more inclined to the 

Dr. Brewster, editor of the ' Edinburgh Encyclope- 
dia,' and the well-known author of various philosophical 
works, espoused this hypothesis with much zeal ; and, 
after summing up the evidence in favor of it, he re- 
marks as follows : " These singular resemblances in 
the motions of the greater fragments, and in those of 
the lesser fragments, and the striking coincidences be- 
tween theory and observation in the eccentricity of their 
orbits, in their inclination to the ecliptic, in the position 
of their nodes, and in the places of their perihelia, are 
phenomena which could not possibly result from chance, 
and which concur to prove, with an evidence amount- 
ing almost to demonstration, that the four new planets 
have diverged from one common node, and have there- 
fore composed a single planet." 

The same distinguished writer supposes that some 
of the smallest fragments might even have come within 
reach of the earth's attraction, and by the combined ef- 
fects of their projectile forces and the attraction of the 
earth, be made to revolve around this body as the lar- 
ger fragments are carried around the sun ; and that 
these are in fact the bodies which afford those meteoric 


stones which are occasionally precipitated to the earth. 
It is now a well-ascertained fact, a fact which has been 
many times verified in our own country, that large mete- 
ors, in the shape of fire-balls, traversing the atmosphere, 
sometimes project to the earth masses of stony or ferru- 
ginous matter. Such were the meteoric stones which 
fell at Weston, in Connecticut, in 1807, of which a full 
and interesting account was published, after a minute 
examination of the facts, by Professors Silliman and 
Kingsley, of Yale College. Various accounts of sim~ 
ilar occurrences may be found in different volumes of 
the American Journal of Science. It is for the pro- 
duction of these wonderful phenomena that Dr. Brews- 
ter supposes the explosion of the planet, which, accord- 
ing to Dr. Olbers, produced the asteroids, accounts. 
Others, however, as Sir John Herschel, have been dis- 
posed to ascribe very little weight to the doctrine of 



" God of the rolling orbs above ! 
Thy name is written clearly bright 
In the warm day's unvarying blaze, 
Or evening's golden shower of light ^ 
For every fire that fronts the sun, 
And every spark that walks alone 
Around the utmost verge of heaven, 
Was kindled at thy burning throne." Peabody. 

IF we could stand upon the sun and view the plan- 
etary motions, they would appear to us as simple as the 
motions of equestrians riding with different degrees of 
speed around a large ring, of which we occupied the 
centre. We should see all the planets coursing each 
other from west to east, through the same great high- 
way, (the Zodiac,) no one of them, with the exception 
of the asteroids, deviating more than seven degrees 
from the path pursued by the earth. Most of them, in- 


deed, would always be seen moving much nearer than 
that to the ecliptic. We should see the planets mov- 
ing on their way with various degrees of speed. Mer- 
cury would make the entire circuit in about three 
months, hurrying on his course with a speed about one 
third as great as that by which the moon revolves 
around the earth. The most distant planets, on the 
other hand, move at so slow a pace, that we should see 
Mercury, Venus, the Earth, and Mars, severally overtak- 
ing them a great many times, before they had com- 
pleted their revolutions. But though the movements of 
some were comparatively rapid, and of others extremely 
slow, yet they would not seem to differ materially, in 
other respects : each would be making a steady and 
nearly uniform march along the celestial vault. 

Such would be the simple and harmonious motions 
of the planets, as they would be seen from the sun, the 
centre of their motions ; and such they are, in fact. But 
two circumstances conspire to make them appear ex- 
ceedingly different from these, and vastly more compli- 
cated ; one is, that we view them uut of the centre or 
their motions ; the other, that we are ourselves in mo- 
tion. I have already explained to you the effect which 
these two causes produce on the apparent motions of 
the inferior planets, Mercury and Venus. Let us now 
see how they effect those of the superior planets, Mars, 
Jupiter, Saturn, and Uranus. 

Orreries, or machines intended to exhibit a model 
of the solar system, are sometimes employed to give a 
popular view of the planetary motions ; but they oftener 
mislead than give correct ideas. They may assist re- 
flection, but they can never supply its place. The im- 
possibility of representing things in their just propor- 
tions will be evident, when we reflect that, to do this, 
if in an orrery we make Mercury as large as a cherry, 
we should have to represent the sun six feet in diam- 
eter. If we preserve the same proportions, in regard to 
distance, we must place Mercury two hundred and fif- 
ty feet, and Uranus twelve thousand five hundred feet, 


or more than two miles from the sun. The mind of 
the student of astronomy must, therefore, raise itself from 
such imperfect representations of celestial phenomena, 
as are afforded by artificial mechanism, and, transferring 
his contemplations to the celestial regions themselves, 
he must conceive of the sun and planets as bodies that 
bear an insignificant ratio to the immense spaces in 
which they circulate, resembling more a few little birds 
flying in the open sky, than they do the crowded ma- 
chinery of an orrery. 

The real motions of the planets, indeed, or such as 
orreries usually exhibit, are very easily conceived of, as 
before explained ; but the apparent motions are, for 
the most part, entirely different from these. The ap- 
parent motions of the inferior planets have been already 
explained. You will recollect that Mercury and Ve- 
nus move backwards and forwards across the sun, the 
former never being seen further than twenty-nine de- 
grees, and the latter never more than about forty-seven 
degrees, from that luminary ; that, while passing from 
the greatest elongation on one side, to the greatest elon- 
gation on the other side, through the superior conjunc- 
tion, the apparent motions of these planets are acceler- 
ated by the motion of the earth ; but that, while mov- 
ing through the inferior conjunction, at which time their 
motions are retrograde, they are apparently retarded 
by the earth's motion. Let us now see what are the 
apparent motions of the superior planets. 

Let A, B, C, Fig. 62, page 294, represent the earth 
in different positions in its orbit, M, a superior planet, as 
Mars, and N R, an arc of the concave sphere of the heav- 
ens. First, suppose the planet to remain at rest in M, 
and let us see what apparent motions it will receive from 
the real motions of the earth. When the earth is at B, 
it will see the planet in the heavens at N ; and as the 
earth moves successively through C, D, E, F, the planet 
will appear to move through O, P, Q, R. B and F are the 
two points of greatest elongation of the earth from the 
sun, as seen from the planet ; hence, between these 



two points, while passing through its orbit most remote 
from the planet, (when the planet is seen in superior 
conjunction,) the earth, by its own motion, gives an 
apparent motion to the planet in the order of the signs ; 
that is, the apparent motion given by the real motion 
of the earth is direct. But in passing from F to B 
through A, when the planet is seen in opposition, the 
apparent motion given to the planet by the earth's mo- 
tion is from R to N, and is therefore retrograde. As 
the arc described by the earth, when the motion is di- 
rect, is much greater than when the motion is retro- 
grade, while the apparent arc of the heavens described 
by the planet from N to R, in the one case, and from 
R to N, in the other, is the same in both cases, the ret- 
rograde motion is much swifter than the direct, being 
performed in much less time. 

But the superior planets are not in fact at rest, as we 
have supposed, but are all the while moving eastward, 
though with a slower motion than the earth. Indeed, 


with respect to the remotest planets, as Saturn and 
Uranus, the forward motion is so exceedingly slow, that 
the above representation is nearly true for a single year. 
Still , the effect of the real motions of all the superior plan- 
ets, eastward, is to increase the direct apparent motion 
communicated by the earth, and to diminish the retro- 
grade motion. This will be evident from inspecting 
the figure ; for if the planet actually moves eastward 
while it is apparently carried eastward by the earth's 
motion, the whole motion eastward will be equal to the 
sum of the two ; and if, while it is really moving east- 
ward, it is apparently carried westward still more by the 
earth's motion, the retrograde movement will equal the 
difference of the two. 

If Mars stood still while the earth went round the 
sun, then a second opposition, as at A, would occur at 
the end of one year from the first ; but, while the earth 
is performing this circuit, Mars is also moving the 
same way, more than half as fast ; so that, when the 
earth returns to A, the planet has already performed 
more than half the same circuit, and will have complet- 
ed its whole revolution before the earth comes up with 
it. Indeed Mars, after having been seen once in oppo- 
sition, does not come into opposition again until after 
two years and fifty days. And since the planet is then 
comparatively near to us, as at M, while the earth is at 
A, and appears very large and bright, rising unexpect- 
edly about the time the sun sets, he surprises the world 
as though it were some new celestial body. But on 
account of the slow progress of Saturn and Uranus, we 
find, after having performed one circuit around the sun, 
that they are but little advanced beyond where we left 
them at the last opposition. The time between one 
opposition of Saturn and another is only a year and 
thirteen days. 

It appears, therefore, that the superior planets stead- 
ily pursue their course around the sun, but that their 
apparent retrograde motion, when in opposition, is occa- 
sioned by our passing by them with a swifter motion, of 


which we are unconscious, like the apparent backward 
motion of a vessel, when we overtake it and pass by it 
rapidly in a steam-boat. 

Such are the real and the apparent motions of the 
planets. Let us now turn our attention to the laws of 
the planetary orbits. 

There are three great principles, according to which 
the motions of the earth and all the planets around the 
sun are regulated, called KEPLER'S LAWS, having been 
first discovered by the astronomer whose name they 
bear. They may appear to you, at first, dry and ob- 
scure ; yet they will be easily understood from the ex- 
planations which follow ; and so important have they 
proved in astronomical inquiries, that they have ac- 
quired for their renowned discoverer the appellation of 
the 'Legislator of the Skies. 1 We will consider each 
of these laws separately ; and, for the sake of rendering 
the explanation clear and intelligible, I shall perhaps 
repeat some things that have been briefly mentioned 

FIRST LAW. The orbits of the earth and all the 
planets are ellipses, having the sun in the common 
focus. In a circle, all the diameters are equal to one 
another ; but if we take a metallic wire or hoop, and 
draw it out on opposite sides, we elongate it into an 
ellipse, of which the different diameters are very une- 
qual. That which connects the points most distant 
from each other is called the transverse, and that which 
is at right angles to this is called the conjugate, axis. 
Thus, A B, Fig. 63, is the transverse axis, and C D, 
the conjugate of the ellipse ABC. By such a proc- 
ess of elongating the circle into an ellipse, the centre 
of the circle may be conceived of as drawn opposite 
ways to E and F, each of which becomes a focus, and 
both together are called the foci of the ellipse. The 
distance G E, or G F, of the focus from the centre is 
called the eccentricity of the ellipse ; and the ellipse is 
said to be more or less eccentric, as the distance of the 
focus from the centre is greater or less. Figure 64, 


represents such a collection of ellipses around the com- 
mon focus F, the innermost, A G D, having a small ec- 
centricity, or varying little from a circle, while the out- 
ermost, A C B, is an eccentric ellipse. The orbits of all 
the bodies that revolve about the sun, both planets 
and comets, have, in like manner, a common focus, in 
which the sun is situated, but they differ in eccentricity. 
Most of the planets have orbits of very little eccentric- 



ity, differing little from circles, but comets move in very 
eccentric ellipses. The earth's path around the sun 
varies so little from a circle, that a diagram represent- 
ing it truly would scarcely be distinguished from a per- 
fect circle ; yet, when the comparative distances of the 
sun from the earth are taken at different seasons of the 
year, we find that the difference between their greatest 
and least distances is no less than three millions of miles. 

SECOND LAW. The radius vector of the earth, or 
of any planet, describes equal areas in equal times. 
You will recollect that the radius vector is a line drawn 
from the centre of the sun to a planet revolving about 
the sun. This definition I have somewhere given you 
before, and perhaps it may appear to you like needless 
repetition to state it again. In a book designed for 
systematic instruction, where all the articles are dis- 
tinctly numbered, it is commonly sufficient to make a 
reference back to the article where the point in ques- 
tion is explained ; but I think, in Letters like these, you 
will bear with a little repetition, rather than be at the 
trouble of turning to the Index and hunting up a defi- 
nition long since given. 

In Figure 65, E a, E 6, E c, &c., are successive repre- 
sentations of the radius vector. Now, if a planet sets 

Fig. 65. 




out from #, and travels round the sun in the direction 
of a b c, it will move faster when nearer the sun, as at a, 
than when more remote from it, as at m ; yet, if a & 
and m n be arcs described in equal times, then, accord- 
ing to the foregoing law, the space E a b will be equal 
to the space Emn\ and the same is true of all the 
other spaces described in equal times. Although the 
figure E a b is much shorter than E m n, yet its greater 
breadth exactly counterbalances the greater length of 
those figures which are described by the radius vector 
where it is longer. 

THIRD LAW. The squares of the periodical times 
are as the cubes of the mean distances from the sun. 
The periodical time of a body is the time it takes to 
complete its orbit, in its revolution about the sun. 
Thus the earth's periodic time is one year, and that 
of the planet Jupiter about twelve years. As Jupiter 
takes so much longer time to travel round the sun than 
the earth does, we might suspect that his orbit is larger 
than that of the earth, and of course, that he is at a 
greater distance from the sun ; and our first thought 
might be, that he is probably twelve times as far off; 
but Kepler discovered that the distance does not in- 
crease as fast as the times increase, but that the planets 
which are more distant from the sun actually move 
slower than those which are nearer. After trying a 
great many proportions, he at length found that, if we 
take the squares of the periodic times of two planets, 
the greater square contains the less, just as often as 
the cube of the distance of the greater contains that 
of the less. This fact is expressed by saying, that the 
squares of the periodic times are to one another as the 
cubes of the distances. 

This law is of great use in determining the distance 
of the planets from the sun. Suppose, for example, 
that we wish to find the distance of Jupiter. We can 
easily determine, from observation, what is Jupiter's pe- 
riodical time, for we can actually see how long it takes 
for Jupiter, after leaving a certain part of the heavens, 


to come round to the same part again. Let this pe- 
riod be twelve years. The earth's period is of course 
one year ; and the distance of the earth, as determined 
from the sun's horizontal parallax, as already explained, 
is about ninety-five millions of miles. Now, we have 
here three terms of a proportion to find the fourth, and 
therefore the solution is merely a simple case of the 
rule of three. Thus : the square of 1 year : square 
of 12 years : : cube of 95,000,000 : cube of Jupiter's 
distance. The three first terms being known, we have 
only to multiply together the second and third and di- 
vide by the first, to obtain the fourth term, which will 
give us the cube of Jupiter's distance from the sun ; and 
by extracting the cube root of this sum, we obtain the 
distance itself. In the same manner we may obtain the 
respective distances of all the other planets. 

So truly is this a law of the solar system, that it 
holds good in respect to the new planets, which have 
been discovered since Kepler's time, as well as in the 
case of the old planets. It also holds good in respect 
to comets, and to all bodies belonging to the solar sys- 
tem, which revolve around the sun as their centre of 
motion. Hence, it is justly regarded as one of the 
most interesting and important principles yet develop- 
ed in astronomy. 

But who was this Kepler, that gained such an extra- 
ordinary insight into the laws of the planetary system, 
as to be called the ' Legislator of the Skies ?' John 
Kepler was one of the most remarkable of the human 
race, and I think I cannot gratify or instruct you more, 
than by occupying the remainder of this Letter with 
some particulars of his history. 

Kepler was a native of Germany. He was born in 
the Duchy of Wurtemberg, in 1571. As Copernicus, 
Tycho Brahe, Galileo, Kepler, and Newton, are names 
that are much associated in the history of astronomy, 
let us see how they stood related to each other in point 
of time. Copernicus was bom in 1473 ; Tycho, in 
1546 ; Galileo, in 1564 ; Kepler, in 1571 ; and Newton, 

KEPLER. 301 

in 1642. Hence, Copernicus was seventy-three years 
before Tycho, and Tycho ninety-six years before New- 
ton. They all lived to an advanced age, so that Ty- 
cho, Galileo, and Kepler, were contemporary for many 
years; and Newton, as I mentioned in the sketch I 
gave you of his life, was born the year that Galileo died. 

Kepler was born of parents who were then in hum- 
ble circumstances, although of noble descent. Their 
misfortunes, which had reduced them to poverty, seem 
to have been aggravated by their own unhappy disposi- 
tions ; for his biographer informs us, that " his mother 
was treated with a degree of barbarity by her husband 
and brother-in-law, that was hardly exceeded by her 
own perverseness." It is fortunate, therefore, that Kep- 
ler, in his childhood, was removed from the immediate 
society and example of his parents, and educated at a 
public school at the expense of the Duke of Wurtem- 
berg. He early imbibed a taste for natural philosophy, 
but had conceived a strong prejudice against astrono- 
my, and even a contempt for it, inspired, probably, by 
the arrogant and ridiculous pretensions of the astrolo- 
gers, who constituted the principal astronomers of his 
country. A vacant post, however, of teacher of as- 
tronomy, occurred when he was of a suitable age to fill 
it, and he was compelled to take it by the authority of 
his tutors, though with many protestations, on his part, 
wishing to be provided for in some other more brilliant 

Happy is genius, when it lights on a profession en- 
tirely consonant to its powers, where the objects suc- 
cessively presented to it are so exactly suited to its na- 
ture, that it clings to them as the loadstone to its kin- 
dred metal among piles of foreign ores. Nothing could 
have been more congenial to the very mental constitu- 
tion of Kepler, than the study of astronomy, a science 
where the most capacious understanding may find scope 
in unison with the most fervid imagination. 

Much as has been said against hypotheses in philos- 
ophy, it is nevertheless a fact, that some of the greatest 
26 L. A. 


truths have been discovered in the pursuit of hypoth- 
eses, in themselves entirely false ; truths, moreover, far 
more important than those assumed by the hypotheses ; 
as Columbus, in searching for a northwest passage to 
India, discovered a new world. Thus Kepler groped 
his way through many false and absurd suppositions, to 
some of the most sublime discoveries ever made by 
man. The fundamental principle which guided him 
was not, however, either false or absurd. It was, that 
God, who made the world, had established, throughout 
all his works, fixed laws, laws that are often so defi- 
nite as to be capable of expression in exact numerical 
terms. In accordance with these views, he sought for 
numerical relations in the disposition and arrangement 
of the planets, in respect to their number, the times of 
their revolution, and their distances from one another. 
Many, indeed, of the subordinate suppositions which 
he made, were extremely fanciful ; but he tried his own 
hypotheses by a rigorous mathematical test, wherever 
he could apply it ; and as soon as he discovered that a 
supposition would not abide this test, he abandoned it 
without the least hesitation, and adopted others, which 
he submitted to the same severe trial, to share, perhaps, 
the same fate. " After many failures," he says, " I was 
comforted by observing that the motions, in every case, 
seemed to be connected with the distances ; and that, 
when there was a great gap between the orbits, there 
was the same between the motions. And I reasoned 
that, if God had adapted motions to the orbits in some 
relation to the distances, he had also arranged the dis- 
tances themselves in relation to something else." 

In two years after he commenced the study of as- 
tronomy, he published a book, called the ' Mysterium 
Cosmographicwm,' a name which implies an explana- 
tion of the mysteries involved in the construction of the 
universe. This work was full of the wildest specula- 
tions and most extravagant hypotheses, the most re- 
markable of which was, that the distances of the plan- 
ets from the sun are regulated by the relations which 

KEPLER. 303 

subsist between the five regular solids. It is well 
known to geometers, that there are and can be only 
five regular solids. These are, first, the tetraedron, a 
four-sided pyramid, all whose sides are equal and simi- 
lar triangles ; secondly, the cube, contained by six 
equal squares ; thirdly, an octaedron, an eight-sided 
figure, consisting of two tetraedrons joined together at 
their bases ; fourthly, a dedecaedron, having twelve five- 
sided or pentagonal faces ; and, fifthly, an icosaedron, 
contained by twenty equal and similar triangles. You 
will be much at a loss, I think, to imagine what rela- 
tion Kepler could trace between these strange figures 
and the distances of the several planets from the sun. 
He thought he discovered a connexion between those 
distances and the spaces which figures of this kind 
would occupy, if interposed in certain ways between 
them. Thus, he says the Earth is a circle, the meas- 
ure of all ; round it describe a dodecaedron, and the 
circle including this will be the orbit of Mars. Round 
this circle describe a tetraedron, and the circle inclu- 
ding this will be the orbit of Jupiter. Describe a cube 
round this, and the circle including it will be the orbit 
of Saturn. Now, inscribe in the earth an icosaedron, 
and the circle included in this will give the orbit of 
Venus. In this inscribe an octaedron, and the circle 
included in this will be the orbit of Mercury. On this 
supposed discovery Kepler exults in the most enthusi- 
astic expressions. "The intense pleasure I have re- 
ceived from this discovery never can be told in words. 
I regretted no more time wasted ; I tired of no labor ; 
I shunned no toil of reckoning ; days and nights I spent 
in calculations, until I could see whether this opinion 
would agree with the orbits of Copernicus, or whether 
my joy was to vanish into air. I willingly subjoin that 
sentiment of Archytas, as given by Cicero ; ' If I could 
mount up into heaven, and thoroughly perceive the 
nature of the world and the beauty of the stars, that 
admiration would be without a charm for me, unless I 
had some one like you, reader, candid, attentive, and 


eager for knowledge, to whom to describe it.' If you 
acknowledge this feeling, and are candid, you will re- 
frain from blame, such as, not without cause, I antici- 
pate ; but if, leaving that to itself, you fear, lest these 
things be not ascertained, and that I have shouted tri- 
umph before victory, at least approach these pages, 
and learn the matter in consideration : you will not 
find, as just now, new and unknown planets interpos- 
ed ; that boldness of mine is not approved ; but those 
old ones very little loosened, and so furnished by the 
interposition (however absurd you may think it) of rec- 
tilinear figures, that in future you may give a reason 
to the rustics, when they ask for the hooks which keep 
the skies from falling." 

When Tycho Brahe, who had then retired from his 
famous Uraniburg, and was settled in Prague, met with 
this work of Kepler's, he immediately recognised under 
this fantastic garb the lineaments of a great astronomer. 
He needed such an unwearied and patient calculator 
as he perceived Kepler to be, to aid him in his labors, 
in order that he might devote himself more unreserved- 
ly to the taking of observations, an employment in 
which he delighted, and in which, as I mentioned, in 
giving you a sketch of his history, he excelled all 
men of that and preceding ages. Kepler, therefore, at 
the express invitation of Tycho, went to Prague, and 
joined him in the capacity of assistant. Had Tycho 
been of a nature less truly noble, he might have looked 
with contempt on one who had made so few observa- 
tions, and indulged so much in wild speculation ; or he 
might have been jealous of a rising genius, in which he 
descried so many signs of future eminence as an as- 
tronomer ; but, superior to all the baser motives, he 
extends to the young aspirant the hand of encourage- 
ment, in the following kind invitation : " Come not as 
a stranger, but as a very welcome friend ; come, and 
share in my observations, with such instruments as I 
have with me." 

Several years previous to this, Kepler, after one or 

KEPLER. 305 

two unsuccessful trials, had found him a wife, from 
whom he expected a considerable fortune ; but in this 
he was disappointed ; and so poor was he, that, when 
on his journey to Prague, in company with his wife, 
being taken sick, he was unable to defray the expenses 
of the journey, and was forced to cast himself on the 
bounty of Tycho. 

In the course of the following year, while absent from 
Prague, he fancied that Tycho had injured him, and 
accordingly addressed to the noble Dane a letter full 
of insults and reproaches. A mild reply from Tycho 
opened the eyes of Kepler to his own ingratitude. His 
better feelings soon returned, and he sent to his great 
patron this humble apology: "Most noble Tycho! 
How shall I enumerate, or rightly estimate, your bene- 
fits conferred on me ! For two months you have lib- 
erally and gratuitously maintained me, and my whole 
family ; you have provided for all my wishes ; you have 
done me every possible kindness ; you have communi- 
cated to me every thing you hold most dear ; no one, by 
word or deed, has intentionally injured me in any thing ; 
in short, not to your own children, your wife, or your- 
self, have you shown more indulgence than to me. 
This being so, as I am anxious to put upon record, I 
cannot reflect, without consternation, that I should have 
been so given up by God to my own intemperance, as 
to shut my eyes on all these benefits ; that, instead of 
modest and respectful gratitude, I should indulge for 
three weeks in continual moroseness towards all your 
family, and in headlong passion and the utmost inso- 
lence towards yourself, who possess so many claims on 
my veneration, from your noble family, your extraordi- 
nary learning, and distinguished reputation. Whatever 
I have said or written against the person, the fame, the 
honor, and the learning, of your Excellency ; or what- 
ever, in any other way, I have injuriously spoken or 
written, (if they admit no other more favorable inter- 
pretation,) as to my grief I have spoken and written 
many things, and more than I can remember ; all and 


every thing I recant, and freely and honestly declare and 
profess to be groundless, false, and incapable of proof." 
This was ample satisfaction to the generous Tycho. 

" To err is human : to forgive, divine." 

On Kepler's return to Prague, he was presented to 
the Emperor by Tycho, and honored with the title of 
Imperial Mathematician. This was in 1601, when he 
was thirty years of age. Tycho died shortly after, and 
Kepler succeeded him as principal mathematician to 
the Emperor ; but his salary was badly paid, and he 
suffered much from pecuniary embarrassments. Al- 
though he held the astrologers, or those who told for- 
tunes by the stars, in great contempt, yet he entertained 
notions of his own, on the same subject, quite as ex- 
travagant, and practised the art of casting nativities, to 
eke out a support for his family. 

When Galileo began to observe with his telescope, 
and announced, in rapid succession, his wonderful dis- 
coveries, Kepler entered into them with his character- 
istic enthusiasm, although they subverted many of his 
favorite hypotheses. But such was his love of truth, 
that he was among the first to congratulate Galileo, and 
a most engaging correspondence was carried on between 
these master-spirits. 

The first planet, which occupied the particular atten- 
tion of Kepler, was Mars, the long and assiduous study 
of whose motions conducted him at length to the dis- 
covery of those great principles called c Kepler's Laws. 7 
Rarely do we meet with so remarkable a union of a 
vivid fancy with a profound intellect. The hasty and 
extravagant suggestions of the former were submitted 
to the most laborious calculations, some of which, that 
were of great length, he repeated seventy times. This 
exuberance of fancy frequently appears in his style of 
writing, which occasionally assumes a tone ludicrously 
figurative. He seems constantly to contemplate Mars 
as a valiant hero, who had hitherto proved invincible, 
and who would often elude his own efforts to conquer 

KEPLER. 307 

him. " While thus triumphing over Mars, and prepar- 
ing for him, as for one altogether vanquished, tabular 
prisons, and equated, eccentric fetters, it is buzzed 
here and there, that the victory is vain, and that the 
war is raging anew as violently as before. For the ene- 
my, left at home a despised captive, has burst all the 
chains of the equation, and broken forth of the prisons 
of the tables. Skirmishes routed my forces of physical 
causes, and, shaking off the yoke, regained their liberty. 
And now, there was little to prevent the fugitive enemy 
from effecting a junction with his own rebellious sup- 
porters, and reducing me to despair, had I not sudden- 
ly sent into the field a reserve of new physical reason- 
ings, on the rout and dispersion of the veterans, and 
diligently followed, without allowing the slightest res- 
pite, in the direction in which he had broken out." 

But he pursued this warfare with the planet until he 
gained a full conquest, by the discovery of the first two 
of his laws, namely, that he revolves in an elliptical 
orbit, and that his radius vector passes over equal 
spaces in equal times. 

Domestic troubles, however, involved him in the 
deepest affliction. Poverty, the loss of a promising and 
favorite son, the death of his wife, after a long illness ; 
these were some of the misfortunes that clustered 
around him. Although his first marriage had been an 
unhappy one, it was not consonant to his genius to 
surrender any thing with only a single trial. Accord- 
ingly, it was not long before he endeavored to repair 
his loss by a second alliance. He commissioned a 
number of his friends to look out for him, and he soon 
obtained a tabular list of eleven ladies, among whom 
his affections wavered. The progress of his courtship 
is thus narrated in the interesting 'Life' contained in 
the ' Library of Useful Knowledge.' It furnishes so 
fine a specimen of his eccentricities, that I cannot deny 
myself the pleasure of transcribing the passage for your 
perusal. It is taken from an account which Kepler 
himself gave in a letter to a friend. 


" The first on the list was a widow, an intimate friend 
of his first wife and who, on many accounts, appeared 
a most eligible match. At first, she seemed favorably 
inclined to the proposal : it is certain that she took 
time to consider it, but at last she very quietly excused 
herself. Finding her afterwards less agreeable in per- 
son than he had anticipated, he considered it a fortu- 
nate escape, mentioning, among other objections, that 
she had two marriageable daughters, whom, by the way, 
he had got on his list for examination. He was much 
troubled to reconcile his astrology with the fact of his 
having taken so much pains about a negotiation not 
destined to succeed. He examined the case profes- 
sionally. ' Have the stars,' says he, ' exercised any in- 
fluence here ? For, just about this time, the direction 
of the mid-heaven is in hot opposition to Mars, and the 
passage of Saturn through the ascending point of the 
zodiac, in the scheme of my nativity, will happen again 
next November and December. But, if these are the 
causes, how do they act ? Is that explanation the true 
one, which I have elsewhere given ? For I can never 
think of handing over to the stars the office of deities, 
to produce effects. Let us, therefore, suppose it ac- 
counted for by the stars, that at this season I am vio- 
lent in my temper and affections, in rashness of belief, 
in a show of pitiful tender-heartedness, in catching at 
reputation by new and paradoxical notions, and the 
singularity of my actions ; in busily inquiring into, and 
weighing, and discussing, various reasons ; in the unea- 
siness of my mind, with respect to my choice. I thank 
God, that that did not happen which might have hap- 
pened ; that this marriage did not take place. Now 
for the others.' Of these, one was too old ; another, in 
bad health ; another, too proud of her birth and quar- 
terings ; a fourth had learned nothing but showy ac- 
complishments, not at all suitable to the kind of life she 
would have to lead with him. Another grew impatient, 
and married a more decided admirer while he was hes- 
itating. < The mischief,' says he, ' in all these attach- 

KEPLER. 309 

ments was, that, whilst I was delaying, comparing, and 
balancing, conflicting reasons, every day saw me in- 
flamed with a new passion.' By the time he reached 
No. 8, of his list, he found his match in this respect. 
' Fortune has avenged herself at length on my doubtful 
inclinations. At first, she was quite complying, and 
her friends also. Presently, whether she did or did 
not consent, not only I, but she herself, did not know. 
After the lapse of a few days, came a renewed promise, 
which, however, had to be confirmed a third time : and, 
four days after that, she again repented her conforma- 
tion, and begged to be excused from it. Upon this, I 
gave her up, and this time all my counsellors were of 
one opinion.' This was the longest courtship in the 
list, having lasted three whole months ; and, quite dis- 
heartened by its bad success, Kepler's next attempt was 
of a more timid complexion. His advances to No. 9 
were made by confiding to her the whole story of his 
recent disappointment, prudently determining to be 
guided in his behavior, by observing whether the treat- 
ment he experienced met with a proper degree of sym- 
pathy. Apparently, the experiment did not succeed ; 
and, when almost reduced to despair, Kepler betook 
himself to the advice of a friend, who had for some 
time past complained that she was not consulted in this 
difficult negotiation. When she produced No. 10, and 
the first visit was paid, the report upon her was as fol- 
lows : ' She has, undoubtedly, a good fortune, is of 
good family, and of economical habits : but her physi- 
ognomy is most horribly ugly ; she would be stared at 
in the streets, not to mention the striking disproportion 
in our figures. I am lank, lean, and spare ; she is 
short and thick. In a family notorious for fatness, she 
is considered superfluously fat.' The only objection to 
No. 1 1 seems to have been, her excessive youth ; and 
when this treaty was broken off, on that account, Kep- 
ler turned his back upon all his advisers, and chose for 
himself one who had figured as No. 5, in his list, to 
whom he professes to have felt attached throughout, 


but from whom the representations of his friends had 
hitherto detained him, probably on account of her hum- 
ble station." 

Having thus settled his domestic affairs, Kepler now 
betook himself, with his usual industry, to his astro- 
nomical studies, and brought before the world the most 
celebrated of his publications, entitled 'Harmonics.' 
In the fifth book of this work he announced his Third 
Law,- that the squares of the periodical times of the 
planets are as the cubes of the distances. Kepler's 
rapture on detecting it was unbounded. " What," says 
he, " I prophesied two-and-twenty years ago, as soon as 
I discovered the five solids among the heavenly orbits ; 
what I firmly believed long before I had seen Ptolemy's 
Harmonics ; what I had promised my friends in the 
title of this book, which I named before I was sure of 
my discovery ; what, sixteen years ago, I urged as a 
thing to be sought; that for which I joined Tycho 
Brahe, for which I settled in Prague, for which I have 
devoted the best part of my life to astronomical con- 
templations ; at length I have brought to light, and 
have recognised its truth beyond my most sanguine ex- 
pectations. It is now eighteen months since I got the 
first glimpse of light, three months since the dawn, very 
few days since the unveiled sun, most admirable to 
gaze on, burst out upon me. Nothing holds me : I 
will indulge in my sacred fury ; I will triumph over 
mankind by the honest confession, that I have stolen 
the golden vases of the Egyptians to build up a taber- 
nacle for my God, far from the confines of Egypt. If 
you forgive me, I rejoice : if you are angry, I can bear 
it ; the die is cast, the book is written, to be read either 
now or by posterity, I care not which. I may well 
wait a century for a reader, as God has waited six 
thousand years for an observer." In accordance with 
the notion he entertained respecting the " music of the 
spheres," he made Saturn and Jupiter take the bass, 
Mars the tenor, the Earth and Venus the counter, and 
Mercury the treble, 

KEPLER. 311 

" The misery in which Kepler lived," says Sir David 
Brewster, in his ' Life of Newton/ " forms a painful 
contrast with the services which he performed for sci- 
ence. The pension on which he subsisted was always in 
arrears ; and though the three emperors, whose reigns he 
adorned, directed their ministers to be more punctual 
in its payment, the disobedience of their commands 
was a source of continual vexation to Kepler. When 
he retired to Silesia, to spend the remainder of his days, 
his pecuniary difficulties became still more harassing. 
Necessity at length compelled him to apply personally 
for the arrears which were due ; and he accordingly set 
out, in 1630, when nearly sixty years of age, for Rat- 
isbon ; but, in consequence of the great fatigue which 
so long a journey on horseback produced, he was seized 
with a fever, which put an end to his life." 

Professor Whewell (in his interesting work on As- 
tronomy and General Physics considered with reference 
to Natural Theology) expresses the opinion that Kep- 
ler, notwithstanding his constitutional oddities, was a 
man of strong and lively piety. His ' Commentaries on 
the Motions of Mars' he opens with the following pas- 
sage : "I beseech my reader, that, not unmindful of 
the Divine goodness bestowed on man, he do with me 
praise and celebrate the wisdom and greatness of the 
Creator, which I open to him from a more inward ex- 
plication of the form of the world, from a searching of 
causes, from a detection of the errors of vision ; and 
that thus, not only in the firmness and stability of the 
earth, he perceive with gratitude the preservation of 
all living things in Nature as the gift of God, but also 
that in its motion, so recondite, so admirable, he ac- 
knowledge the wisdom of the Creator. But him who 
is too dull to receive this science, or too weak to believe 
the Copernican system without harm to his piety, 
him, I say, I advise that, leaving the school of astrono- 
my, and condemning, if he please, any doctrines of the 
philosophers, he follow his own path, and desist from 
this wandering through the universe ; and, lifting up 


his natural eyes, with which he alone can see, pour 
himself out in his own heart, in praise of God the Cre- 
ator ; being certain that he gives no less worship to God 
than the astronomer, to whom God has given to see 
more clearly with his inward eye, and who, for what 
he has himself discovered, both can and will glorify 

In a Life of Kepler, very recently published in his 
native country, founded on manuscripts of his which 
have lately been brought to light, there are given nu- 
merous other examples of a similar devotional spirit. 
Kepler thus concludes his Harmonics : " I give Thee 
thanks, Lord and Creator, that Thou has given me joy 
through Thy creation ; for I have been ravished with 
the work of Thy hands. I have revealed unto mankind 
the glory of Thy works, as far as my limited spirit could 
conceive their infinitude. Should I have brought for- 
ward any thing that is unworthy of Thee, or should I 
have sought my own fame, be graciously pleased to for- 
give me." 

As Galileo experienced the most bitter persecutions 
from the Church of Rome, so Kepler met with much vio- 
lent opposition and calumny from the Protestant clergy 
of his own country, particularly for adopting, in an al- 
manac which, as astronomer royal, he annually publish- 
ed, the reformed calendar, as given by the Pope of 
Rome. His opinions respecting religious liberty, also, 
appear to have been greatly in advance of the times in 
which he lived. In answer to certain calumnies with 
which he was assailed, for his boldness in reasoning 
from the light of Nature, he uttered these memorable 
words : " The day will soon break, when pious sim- 
plicity will be ashamed of its blind superstition ; when 
men will recognise truth in the book of Nature as well 
as in the Holy Scriptures, and rejoice in the two reve- 

COMETS. 313 



1 Fancy now no more 

Wantons on fickle pinions through the skies, 

But, fixed in aim, and conscious of her power, 

Sublime from cause to cause exults to rise, 

Creation's blended stores arranging as she flies." Beattie. 

NOTHING in astronomy is more truly admirable, than 
the knowledge which astronomers have acquired of the 
motions of comets, and the power they have gained of 
predicting their return. Indeed, every thing appertain- 
ing to this class of bodies is so wonderful, as to seem 
rather a tale of romance than a simple recital of facts. 
Comets are truly the knights-errant of astronomy. Ap- 
pearing suddenly in the nocturnal sky, and often drag- 
ging after them a train of terrific aspect, they were, in 
the earlier ages of the world, and indeed until a recent 
period, considered as peculiarly ominous of the wrath 
of Heaven, and as harbingers of wars and famines, of 
the dethronement of monarchs, and the dissolution of 

Science has, it is true, disarmed them of their terrorsy 
and demonstrated that they are under the guidance 
of the same Hand, that directs in their courses the oth- 
er members of the solar system ; but she has, at the 
same time, arrayed them in a garb of majesty peculiar- 
ly her own. 

Although the ancients paid little attention to the or- 
dinary phenomena of Nature, hardly deeming them 
worthy of a reason, yet, when a comet blazed forth, 
fear and astonishment conspired to make it an object 
of the most attentive observation. Hence the aspects 
of remarkable comets, that have appeared at various 
times, have been handed down to us, often with cir- 
cumstantial minuteness, by the historians of different 
ages. The comet which appeared in the year 130, be- 
fore the Christian era, at the birth of Mithridates, is 
27 L. A. 


said to have had a disk equal in magnitude to that of 
the sun. Ten years before this, one was seen, which, 
according to Justin, occupied a fourth part of the sky, 
that is, extended over forty-five degrees, and surpassed 
the sun in splendor. In the year 400, one was seen 
which resembled a sword in shape, and extended from 
the zenith to the horizon. 

Such are some of the accounts of comets of past 
ages ; but it is probable we must allow much for the 
exaggerations naturally accompanying the descriptions 
of objects in themselves so truly wonderful. 

A comet, when perfectly formed, consists of three 
parts, the nucleus, the envelope, and the tail. The nu- 
cleus, or body of the comet, is generally distinguished by 
its forming a bright point in the centre of the head, con- 
veying the idea of a solid, or at least of a very dense, 
portion of matter. Though it is usually exceedingly 
small, when compared with the other parts of the comet, 
and is sometimes wanting altogether, yet it occasionally 
subtends an angle capable of being measured by the 
telescope. The envelope (sometimes called the coma, 
from a Latin word signifying hair, in allusion to its hairy 
appearance) is a dense nebulous covering, which fre- 
quently renders the edge of the nucleus so indistinct, 
that it is extremely difficult to ascertain its diameter 
with any degree of precision. Many comets have no 
nucleus, but present only a nebulous mass, exceedingly 
attenuated on the confines, but gradually increasing in 
density towards the centre. Indeed, there is a regular 
gradation of comets, from such as are composed mere- 
ly of a gaseous or vapory medium, to those which have 
a well-defined nucleus. In some instances on record, 
astronomers have detected with their telescopes small 
stars through the densest part of a comet. The tail is 
regarded as an expansion or prolongation of the coma ; 
and presenting, as it sometimes does, a train of appall- 
ing magnitude, and of a pale, portentous light, it con- 
fers on this class of bodies their peculiar celebrity. 
These several parts are exhibited in Fig. 67, which 

Figures 67, 68. 

COMETS OF 168O AND 1811 

COMETS. 315 

represents the appearance of the comet of 1680. Fig. 
68 also exhibits that of the comet of 1811. 

The number of comets belonging to the solar system, 
is probably very great. Many no doubt escape obser- 
vation, by being above the horizon in the day-time. 
Seneca mentions, that during a total eclipse of the sun, 
which happened sixty years before the Christian era, a 
large and splendid comet suddenly made its appear- 
ance, being very near the sun. The leading particu- 
lars of at least one hundred and thirty have been com- 
puted, and arranged in a table, for future comparison. 
Of these, six are particularly remarkable ; namely, the 
comets of 1680, 1770, and 1811 ; and those which bear 
the names of Halley, Biela, and Encke. The comet 
of 1680 was remarkable, not only for its astonishing 
size and splendor, and its near approach to the sun, 
but is celebrated for having submitted itself to the ob- 
servations of Sir Isaac Newton, and for having enjoy- 
ed the signal honor of being the first comet whose 
elements were determined on the sure basis of math- 
ematics. The comet of 1770 is memorable for the 
changes its orbit has undergone by the action of Jupi- 
ter, as I shall explain to you more particularly hereaf- 
ter. The comet of 1811 was the most remarkable in 
its appearance of all that have been seen in the present 
century. It had scarcely any perceptible nucleus, but 
its train was very long and broad, as is represented in 
Fig. 68. Halley's comet (the same which reappeared 
in 1835) is distinguished as that whose return was first 
successfully predicted, and whose orbit is best determin- 
ed ; and Biela's and Encke's comets are well known for 
their short periods of revolution, which subject them fre- 
quently to the view of astronomers. 

In magnitude and brightness, comets exhibit great 
diversity. History informs us of comets so bright, as to 
be distinctly visible in the day-time, even at noon, and 
in the brightest sunshine. Such was the comet seen at 
Rome a little before the assassination of Julius Caesar. 
The comet of 1680 covered an arc of the heavens of 


ninety-seven degrees, and its length was estimated at 
one hundred and twenty -three millions of miles. That 
of 1811 had a nucleus of only four hundred and twen- 
ty-eight miles in diameter, but a tail one hundred and 
thirty-two millions of miles long. Had it been coiled 
around the earth like a serpent, it would have reached 
round more than five thousand times. Other comets are 
exceedingly small, the nucleus being in one case esti- 
mated at only twenty-five miles ; and some, which are 
destitute of any perceptible nucleus, appear to the 
largest telescopes, even when nearest to us, only as a 
small speck of fog, or as a tuft of down. The majority 
of comets can be seen only by the aid of the telescope. 
Indeed, the same comet has very different aspects, at 
its different returns. Halley's comet, in 1305, was 
described by the historians of that age as the comet 
of terrific magnitude ; (cometa horrendw magnitudi- 
nis;) in 1456 its tail reached from the horizon to the 
zenith, and inspired such terror, that, by a decree of the 
Pope of Rome, public prayers were offered up at noon- 
day in all the Catholic churches, to deprecate the wrath 
of heaven ; while in 1682 its tail was only thirty de- 
grees in length ; and in 1759 it was visible only to the 
telescope until after it had passed its perihelion. At 
its recent return, in 1835, the greatest length of the tail 
was about twelve degrees. These changes in the ap- 
pearance of the same comet are partly owing to the 
different positions of the earth with respect to them, be- 
ing sometimes much nearer to them when they cross its 
track than at others ; also, one spectator, so situated as 
to see the comet at a higher angle of elevation, or in a 
purer sky, than another, will see the train longer than 
it appears to another less favorably situated ; but the 
extent of the changes are such as indicate also a real 
change in magnitude and brightness. 

The periods of comets in their revolutions around the 
sun are equally various. Encke's comet, which has the 
shortest known period, completes its revolution in three 
and one third years ; or, more accurately, in twelve hun- 

COMETS. 317 

dred and eight days; while that of 1811 is estimated 
to have a period of thirty-three hundred and eighty- 
three years. 

The distances to which different comets recede from 
the sun are equally various. While Encke's comet per- 
forms its entire revolution within the orbit of Jupiter, 
Halley's comet recedes from the sun to twice the dis- 
tance of Uranus ; or nearly thirty-six hundred millions 
of miles. Some comets, indeed, are thought to go a 
much greater distance from the sun than this, while 
some are supposed to pass into curves which do not, 
like the ellipse, return into themselves ; and in this case 
they never come back to the sun. (See Fig. 34, page 

Comets shine by reflecting the light of the sun. In 
one or two instances, they have been thought to exhibit 
distinct phases, like the moon, although the nebulous 
matter with which the nucleus is surrounded would 
commonly prevent such phases from being distinctly 
visible, even when they would otherwise be apparent. 
Moreover, certain qualities of polarized light, an af- 
fection by which a ray of light seems to have different 
properties on different sides, enable opticians to decide 
whether the light of a given body is direct or reflected ; 
and M. Arago, of Paris, by experiments of this kind on 
the light of the comet of 1819, ascertained it to be re- 
flected light. 

The tail of a comet usually increases very much as 
it approaches the sun ; and it frequently does not reach 
its maximum until after the perihelion passage. In re- 
ceding from the sun, the tail again contracts, and near- 
ly or quite disappears before the body of the comet is 
entirely out of sight. The tail is frequently divided 
into two portions, the central parts, in the direction of 
the axis, being less bright than the marginal parts. In 
1744 a comet appeared which had six tails spread out 
like a fan. 

The tails of comets extend in a direct line from the 
sun, although more or less curved, like a long quill or 


feather, being convex on the side next to the direction 
in which they are moving, a figure which may result 
from the less velocity of the portion most remote from 
the sun. Expansions of the envelope have also been 
at times observed on the side next the sun ; but these 
seldom attain any considerable length. 

The quantity of matter in comets is exceedingly 
small. Their tails consist of matter of such tenuity, 
that the smallest stars are visible through them. They 
can only be regarded as masses of thin vapor, suscepti- 
ble of being penetrated through their whole substance 
by the sunbeams, and reflecting them alike from their 
interior parts and from their surfaces. It appears per- 
haps incredible, that so thin a substance should be vis- 
ible by reflected light, and some astronomers have held 
that the matter of comets is self-luminous ; but it re- 
quires but very little light to render an object visible in 
the night, and a light vapor may be visible when illu- 
minated throughout an immense stratum, which could 
not be seen if spread over the face of the sky like a 
thin cloud. " The highest clouds that float in our at- 
mosphere," says Sir John Herschel, " must be looked 
upon as dense and massive bodies, compared with the 
filmy and all but spiritual texture of a comet." 

The small quantity of matter in comets is proved by 
the fact, that they have at times passed very near to some 
of the planets, without disturbing their motions in any 
appreciable degree. Thus the comet of 1770, in its way 
to the sun, got entangled among the satellites of Jupi- 
ter, and remained near them four months ; yet it did not 
perceptibly change their motions. The same comet, 
also, came very near the earth ; so that, had its quan- 
tity of matter been equal to that of the earth, it would, 
by its attraction, have caused the earth to revolve in an 
orbit so much larger than at present, as to have in- 
creased the length of the year two hours and forty- 
seven minutes. Yet it produced no sensible effect on 
the length of the year, and therefore its mass, as is 
shown by La Place, could not have exceeded -^W of 

COMETS. 319 

that of the earth, and might have been less than this to 
any extent. It may indeed be asked, what proof we 
have that comets have any matter, and are not mere 
reflections of light. The answer is, that, although they 
are not able by their own force of attraction to disturb 
the motions of the planets, yet they are themselves ex- 
ceedingly disturbed by the action of the planets, and in 
exact conformity with the laws of universal gravitation. 
A delicate compass may be greatly agitated by the vi- 
cinity of a mass of iron, while the iron is not sensibly 
affected by the attraction of the needle. 

By approaching very near to a large planet, a comet 
may have its orbit entirely changed. This fact is strik- 
ingly exemplified in the history of the comet of 1770. 
At its appearance in 1770, its orbit was found to be an 
ellipse, requiring for a complete revolution only five 
and a half years ; and the wonder was, that it had not 
been seen before, since it was a very large and bright 
comet. Astronomers suspected that its path had been 
changed, and that it had been recently compelled to 
move in this short ellipse, by the disturbing force of 
Jupiter and his satellites. The French Institute, there- 
fore, offered a high prize for the most complete investi- 
gation of the elements of this comet, taking into ac- 
count any circumstances which could possibly have 
produced an alteration in its course. By tracing back 
the movements of this comet for some years previous to 
1770, it was found that, at the beginning of 1767, it 
had entered considerably within the sphere of Jupiter's 
attraction. Calculating the amount of this attraction 
from the known proximity of the two bodies, it was 
found what must have been its orbit previous to the 
time when it became subject to the disturbing action 
of Jupiter. It was therefore evident why, as long as it 
continued to circulate in an orbit so far from the cen- 
tre of the system, it was never visible from the earth. 
In January, 1767, Jupiter and the comet happened to 
be very near to one another, and as both were moving 
in the same direction, and nearly in the same plane, 


they remained in the neighborhood of each other for 
several months, the planet being between the comet 
and the sun. The consequence was, that the comet's 
orbit was changed into a smaller ellipse, in which its 
revolution was accomplished in five and a half years. 
But as it approached the sun, in 1779, it happened 
again to fall in with Jupiter. It was in the month of 
June that the attraction of the planet began to have a 
sensible effect ; and it was not until the month of Oc- 
tober following, that they were finally separated. 

At the time of their nearest approach, in August, 
Jupiter was distant from the comet only ^ T of its dis- 
tance from the sun, and exerted an attraction upon it 
two hundred and twenty-five times greater than that of 
the sun. By reason of this powerful attraction, Jupi- 
ter being further from the sun than the comet, the lat- 
ter was drawn out into a new orbit, which even at its 
perihelion came no nearer to the sun than the planet 
Ceres. In this third orbit, the comet requires about 
twenty years to accomplish its revolution ; and being at 
so great a distance from the earth, it is invisible, and 
will for ever remain so, unless, in the course of ages, it 
may undergo new perturbations, and move again in 
some smaller orbit, as before. 

With the foregoing leading facts respecting comets 
in view, I will now explain to you a few things equally 
remarkable respecting their motions. 

The paths of the planets around the sun being near- 
ly circular, we are able to see a planet in every part of 
its orbit. But the case is very different with comets. 
For the greater part of their course, they are wholly 
out of sight, and come into view only while just in the 
neighborhood of the sun. This you will readily see 
must be the case, by inspecting the frontispiece, 
which represents the orbit of Biela's comet, in 1832. 
Sometimes, the orbit is so eccentric, that the place 
of the focus occupied by the sun appears almost at 
the extremity of the orbit. This was the case with the 
orbit of the comet of 1680. Indeed, this comet, at 

COMETS. 321 

its perihelion, came in fact nearer to the sun than the 
sixth part of the sun's diameter, being only one hun- 
dred and forty-six thousand miles from the surface of the 
sun, which, you will remark, is only a little more than half 
the distance of the moon from the earth ; while, at its 
aphelion, it was estimated to be thirteen thousand mil- 
lions of miles from the sun, more than eleven thousand 
millions of miles beyond the planet Uranus. Its veloci- 
ty, when nearest the sun, exceeded a million of miles an 
hour. To describe such an orbit as was assigned to it 
by Sir Isaac Newton, would require five hundred and 
seventy-five years. During all this period, it was entire- 
ly out of view to the inhabitants of the earth, except the 
few months, while it was running down to the sun from 
such a distance as the orbit of Jupiter and back. The 
velocity of bodies moving in such eccentric orbits dif- 
fers widely in different parts of their orbits. In the 
remotest parts it is so slow, that years would be requir- 
ed to pass over a space equal to that which it would 
run over in a single day, when near the sun. 

The appearances of the same comet at different pe- 
riods of its return are so various, that we can never 
pronounce a given comet to be the same with one that 
has appeared before, from any peculiarities in its phys- 
ical aspect, as from its color, magnitude, or shape ; since, 
in all these respects, it is very different at different re- 
turns ; but it is judged to be the same if its path through 
the heavens, as traced among the stars, is the same. 

The comet whose history is the most interesting, and 
which both of us have been privileged to see, is Hal- 
ley's. Just before its latest visit, in 1835, its return 
was anticipated with so much expectation, not only 
by astronomers, but by all classes of the community, 
that a great and laudable eagerness universally prevail- 
ed, to learn the particulars of its history. The best 
summary of these, which I met with, was given in the 
Edinburgh Review for April, 1835. I might content 
myself with barely referring you to that well-written ar- 
ticle ; but, as you may not have the work at hand, and 


would, moreover, probably not desire to read the whole 
article, I will abridge it for your perusal, interspersing 
some remarks of my own. I have desired to give you, 
in the course of these Letters, some specimen of the 
labors of astronomers, and shall probably never be able 
to find a better one. 

It is believed that the first recorded appearance of 
Halley's comet was that which was supposed to sig- 
nalize the birth of Mithridates, one hundred and thirty 
years before the birth of Christ. It is said to have 
appeared for twenty-four days ; its light is said to 
have surpassed that of the sun ; its magnitude to have 
extended over a fourth part of the firmament ; and it 
is stated to have occupied, consequently, about four 
hours in rising and setting. In the year 323, a comet 
appeared in the sign Virgo. Another, according to 
the historians of the Lower Empire, appeared in the 
year 399, seventy-six years after the last, at an interval 
corresponding to that of Halley's comet. The interval 
between the birth of Mithridates and the year 323 
was four hundred and fifty-three years, which would 
be equivalent to six periods of seventy-five and a half 
years. Thus it would seem, that in the interim there 
were five returns of this comet unobserved, or at least 
unrecorded. The appearance in the year 399 was at- 
tended with extraordinary circumstances. It was de- 
scribed in the old writers as a " comet of monstrous size 
and appalling aspect, its tail seeming to reach down to 
the ground." The next recorded appearance of a com- 
et agreeing with the ascertained period marks the tak- 
ing of Rome, in the year 550, an interval of one hun- 
dred and fifty-one years, or two periods of seventy-five 
and a half years having elapsed. One unrecorded return 
must, therefore, have taken place in the interim. The 
next appearance of a comet, coinciding with the assigned 
period, is three hundred and eighty years afterwards ; 
namely, in the year 930, five revolutions having been 
completed in the interval. The next appearance is re- 
corded in the year 1005, after an interval of a single 

COMETS. 323 

period of seventy-five years. Three revolutions would 
now seem to have passed unrecorded, when the comet 
again makes its appearance in 1230. In this, as well 
as in former appearances, it is proper to state, that the 
sole test of identity of these comets with that of Halley 
is the coincidence of the times, as near as historical 
records enable us to ascertain, with the epochs at 
which the comet of Halley might be expected to ap- 
pear. That such evidence, however, is very imperfect, 
must be evident, if the frequency of cometary appear- 
ances be considered, and if it be remembered, that hith- 
erto we find no recorded observations, which could 
enable us to trace, even with the rudest degree of 
approximation, the paths of those comets, the times of 
whose appearances raise a presumption of their identi- 
ty with that of Halley. We now, however, descend to 
times in which more satisfactory evidence may be ex- 

In the year 1305, a year in which the return of Hal- 
ley's comet might have been expected, there is record- 
ed a comet of remarkable character : " A comet of ter- 
rific dimensions made its appearance about the time 
of the feast of the Passover, which was followed by a 
Great Plague." Had the terrific appearance of this 
body alone been recorded, this description might have 
passed without the charge of great exaggeration ; but 
when we find the Great Plague connected with it as a 
consequence, it is impossible not to conclude, that the 
comet was seen by its historians through the magnify- 
ing medium of the calamity which followed it. Anoth- 
er appearance is recorded in the year 1380, unaccom- 
panied by any other circumstance than its mere date. 
This, however, is in strict accordance with the ascer- 
tained period of Halley's comet. 

We now arrive at the first appearance at which ob- 
servations were taken, possessing sufficient accuracy to 
enable subsequent investigators to determine the path 
of the comet ; and this is accordingly the first comet 
the identity of which with the comet of Halley can 


be said to be conclusively established. In the year 
1456, a comet is stated to have appeared " of unheard 
of magnitude ;" it was accompanied by a tail of extra- 
ordinary length, which extended over sixty degrees, (a 
third part of the heavens,) and continued to be seen 
during the whole month of June. The influence which 
was attributed to this appearance renders it probable, 
that in the record there is more or less of exaggeration. 
It was considered as the celestial indication of the rap- 
id success of Mohammed the Second, who had taken 
Constantinople, and struck terror into the whole Chris- 
tian world. Pope Calixtus the Second levelled the 
thunders of the Church against the enemies of his 
faith, terrestrial and celestial ; and in the same Bull ex- 
communicated the Turks and the comet ; and, in order 
that the memory of this manifestation of his power 
should be for ever preserved, he ordained that the bells 
of all the churches should be rung at mid-day, a cus- 
tom which is preserved in those countries to our times. 

The extraordinary length and brilliancy which was 
ascribed to the tail, upon this occasion, have led astron- 
omers to investigate the circumstances under which its 
brightness and magnitude would be the greatest possi- 
ble ; and upon tracing back the motion of the comet to 
the year 1456, it has been found that it was then ac- 
tually in the position, with respect to the earth and sun, 
most favorable to magnitude and splendor. So far, 
therefore, the result of astronomical calculation corrob- 
orates the records of history. 

The next return took place in 1531. Pierre Appi- 
an, who first ascertained the fact that the tails of comets 
are usually turned from the sun, examined this comet 
with a view to verify his statement, and to ascertain the 
true direction of its tail. He made, accordingly, nu- 
merous observations upon its position, which, although 
rude, compared with the present standard of accuracy, 
were still sufficiently exact to enable Halley to identify 
this comet with that observed by himself. 

The next return took place in 1607, when the comet 

COMETS* 325 

Was observed by Kepler. This astronomer first saw it 
on the evening of the twenty-sixth of September, when 
it had the appearance of a star of the first magnitude, 
and, to his vision, was without a tail ; but the friends 
who accompanied him had better sight, and distinguish- 
ed the tail. Before three o'clock the following morning 
the tail had become clearly visible, and had acquired 
great magnitude. Two days afterwards, the comet 
was observed by Longomontanus, a distinguished phi- 
losopher of the time. He describes its appearance, to 
the naked eye, to be like Jupiter, but of a paler and 
more obscured light ; that its tail was of considerable 
length, of a paler light than that of the head, and more 
dense than the tails of ordinary comets. 

The next appearance, and that which was observed 
by Halley himself, took place in 1682, a little before 
the publication of the ' Principia.' In the interval 
between 1607 and 1682, practical astronomy had made 
great advances ; instruments of observation had been 
brought to a state of comparative perfection ; numer- 
ous observatories had been established, and the man- 
agement of them had been confided to the most emi- 
nent men in Europe. In 1682, the scientific world 
was therefore prepared to examine the visitor of our 
system with a degree of care and accuracy before un- 

In the year 1686, about four years afterwards, New- 
ton published his ' Principia,' in which he applied to 
the comet of 1680 the general principles of physical 
investigation first promulgated in that work. He ex- 
plained the method of determining, by geometrical 
construction, the visible portion of the path of a body 
of this kind, and invited astronomers to apply these 
principles to the various recorded comets, to discover 
whether some among them might not have appeared 
at different epochs, the future returns of which might 
consequently be predicted. Such was the effect of the 
force of analogy upon the mind of Newton, that, with- 
out awaiting the discovery of a periodic comet, he bold- 

28 L. A. 


ly assumed these bodies to be analogous to planets in 
their revolution round the sun. 

Extraordinary as these conjectures must have appear- 
ed at the time, they were soon strictly realized. Hal- 
ley, who was then a young man, but possessed one of 
the best minds in England, undertook the labor of ex- 
amining the circumstances attending all the comets 
previously recorded, with a view to discover whether 
any, and which of them, appeared to follow the same 
path. Antecedently to the year 1700, four hundred 
and twenty-five of these bodies had been recorded in 
history ; but those which had appeared before the four- 
teenth century had not been submitted to any observa- 
tions by which their paths could be ascertained, at 
least, not with a sufficient degree of precision, to afford 
any hope of identifying them with those of other com- 
ets. Subsequently to the year 1300, however, Halley 
found twenty-four comets on which observations had 
been made and recorded, with a degree of precision 
sufficient to enable him to calculate the actual paths 
which these bodies followed while they were visible. 
He examined, with the most elaborate care, the courses 
of each of these twenty-four bodies ; he found the ex- 
act points at which each one of them crossed the eclip- 
tic, or their nodes ; also the angle which the direction 
of their motion made with that plane, that is, the in- 
clination of their orbits ; he also calculated the nearest 
distance at which each of them approached the sun, or 
their perihelion distance ; and the exact place of the 
body when at that nearest point, that is, the longi- 
tude of the perihelion. These particulars are called 
the elements of a comet, because, when ascertained, 
they afford sufficient data for determining a comet's 
path. On comparing these paths, Halley found that 
one, which had appeared in 1661, followed nearly the 
same path as one which had appeared in 1532. Sup- 
posing, then, these to be two successive appearances of 
the same comet, it would follow, that its period would 
be one hundred and twenty-nine years, reckoning from 



1661. Had this conjecture been well founded, the 
comet must have appeared about the year 1790. No 
comet, however, appeared at or near that time, follow- 
ing a similar path. 

In his second conjecture, Halley was more fortunate, 
as indeed might be expected, since it was formed upon 
more conclusive grounds. He found that the paths of 
comets which had appeared in 1531 and 1607 were 
nearly identical, and that tha^were in fact the same as 
the path followed by the comet observed by himself in 
168-2. He suspected, therefore, that the appearances at 
these three epochs were produced by three successive 
returns of the same comet, and that, consequently, its 
period in its orbit must be about seventy-five and a 
half years. The probability of this conclusion is strik- 
ingly exhibited to the eye, by presenting the elements 
in a tabular form, from which it will at once be seen 
how nearly they correspond at these regular intervals. 


Inclination of 
the orbit. 

Long, of the 

Long. Per. 

Per. Dist. 



17 56 
17 02 
17 42 

49 25 
50 21 

50 48 

301 39 
302 16 
301 36 




1 1 

So little was the scientific world, at this time, pre- 
pared for such an announcement, that Halley himself 
only ventured at first to express his opinion in the form 
of conjecture ; but, after some further investigation of 
the circumstances of the recorded comets, he found 
three which, at least in point of time, agreed with the 
period assigned to the comet of 1682. Collecting con- 
fidence from these circumstances, he announced his 
discovery as the result of observation and calculation 
combined, and entitled to as much confidence as any 
other consequence of an established physical law. 

There were, nevertheless, two circumstances which 
might be supposed to offer some difficulty. First, the 
intervals between the supposed successive returns were 
not precisely equal ; and, secondly, the inclination of 


the comet's path to the plane of the earth's orbit was 
not exactly the same in each case. Halley, however, 
with a degree of sagacity which, considering the state 
of knowledge at the time, cannot fail to excite unqual- 
ified admiration, observed, that it was natural to sup- 
pose that the same causes which disturbed the planeta- 
ry motions must likewise act upon comets ; and that 
their influence would be so much the more sensible 
upon these bodies, becsfltee of their great distances 
from the sun. Thus, as the attraction of Jupiter for 
Saturn was known to affect the velocity of the latter 
planet, sometimes retarding and sometimes accelerating 
it, according to their relative position, so as to affect its 
period to the extent of thirteen days, it might well be 
supposed, that the comet might suffer by a similar at- 
traction an effect sufficiently great, to account for the 
inequality observed in the interval between its succes- 
sive returns : and also for the variation to which the 
direction of its path upon the plane of the ecliptic was 
found to be subject. He observed, in fine, that, as in 
the interval between 1607 and 1682, the comet passed 
so near Jupiter that its velocity must have been aug- 
mented, and consequently its period shortened, by the 
action of that planet, this period, therefore, having been 
only seventy-five years, he inferred that the following 
period would probably be seventy-six years, or upwards ; 
and consequently, that the comet ought not to be ex- 
pected to appear until the end of 1758, or the begin- 
ning of 1759. It is impossible to imagine any quality 
of mind more enviable than that which, in the existing 
state of mathematical physics, could have led to such 
a prediction. The imperfect state of mathematical 
science rendered it impossible for Halley to offer to the 
world a demonstration of the event which he foretold. 
The theory of gravitation, which was in its infancy in 
the time of Halley's investigations, had grown to com- 
parative maturity before the period at which his pre- 
diction could be fulfilled. The exigencies of that the- 
ory gave birth to new and more powerful instruments 

COMETS. 329 

of mathematical inquiry: the differential and integral 
calculus, or the science of fluxions, as it is sometimes 
called, -a branch of the mathematics, expressed by al- 
gebraic symbols, but capable of a much higher reach, 
as an instrument of investigation, than either algebra 
or geometry, was its first and greatest offspring. This 
branch of science was cultivated with an ardor and 
success by which it was enabled to answer all the de- 
mands of physics, and it corrffibuted largely to the ad- 
vancement of mechanical science itself, building upon 
the laws of motion a structure which has since been 
denominated ' Celestial Mechanics.' Newton's discov- 
eries having obtained reception throughout the scientific 
world, his inquiries and his theories were followed up ; 
and the consequences of the great principle of univer- 
sal gravitation were rapidly developed. Since, accord- 
ing to this doctrine, every body in nature attracts and 
is attracted by every other body, it follows, that the 
comet was liable to be acted on by each of the planets, 
as well as by the sun, a circumstance which rendered 
its movements much more difficult to follow, than would 
be the case were it subject merely to the projectile force 
and to the solar attraction. To estimate the time it 
would take for a ship to cross the Atlantic would be 
an easy task, were she subject to only one constant 
wind ; but to estimate, beforehand, the exact influence 
which all other winds and the tides might have upon 
her passage, some accelerating and some retarding her 
course, would present a problem of the greatest diffi- 
culty. Clairaut, however, a celebrated French mathe- 
matician, undertook to estimate the effects that would 
be produced on Halley's comet by the attractions of all 
the planets. His aim was to investigate general rules, 
by which the computation could be made arithmetical- 
ly, and hand them over to the practical calculator, to 
make the actual computations. Lalande, a practical 
astronomer, no less eminent in his own department, 
and who indeed first urged Clairaut to this inquiry, 
undertook the management of the astronomical and 


arithmetical part of the calculation. In this prodigious 
labor (for it was one of most appalling magnitude) he 
was assisted by the wife of an eminent watchmaker in 
Paris, named Lepaute, whose exertions on' this occasion 
have deservedly -registered her name in astronomical 

It is difficult to convey to one who is not convers- 
ant with such investigations, an adequate notion of 
the labor which such an inquiry involved. The calcu- 
lation of the influence of any one planet of the system 
upon any other is itself a problem of some complexity 
and difficulty ; but still, one general computation, de- 
pending upon the calculation of the terms of a certain 
series, is sufficient for its solution. This comparative 
simplicity arises entirely from two circumstances which 
characterize the planetary orbits. These are, that, 
though they are ellipses, they differ very slightly from 
circles ; and though the planets do not move in the 
plane of the ecliptic, yet none of them deviate consid- 
erably from that plane. But these characters do not 
belong to the orbits of comets, which, on the contrary, 
are highly eccentric, and make all possible angles with 
the ecliptic. The consequence of this is, that the cal- 
culation of the disturbances produced in the cometary 
orbits by the action of the planets must be conducted, 
not like the planets, in one general calculation applica- 
ble to the whole orbits, but in a vast number of separ- 
ate calculations ; in which the orbit is considered, as it 
were, bit by bit, each bit requiring a calculation similar 
to the whole orbit of the planet. Now, when it is 
considered that the period of Halley's comet is about 
seventy-five years, and that every portion of its course, 
for two successive periods, was necessary to be calcu- 
lated separately in this way, some notion may be formed 
of the labor encountered by Lalande and Madame Le- 
paute. " During six months," says Lalande, " we cal- 
culated from morning till night, sometimes even at 
meals ; the consequence of which was, that I contract- 
ed an illness which changed my constitution for the 

COMETS. 331 

remainder of my life. The assistance rendered by 
Madame Lepaute was such, that, without her, we never 
could have dared to undertake this enormous labor, in 
which it was necessary to calculate the distance of each 
of the two planets, Jupiter and Saturn, from the com- 
et, and their attraction upon that body, separately, for 
every successive degree, and for one hundred and fifty 

The attraction of a body is proportioned to its quan- 
tity of matter. Therefore, before the attraction exert- 
ed upon the comet, by the several planets within whose 
influence it might fall, could be correctly estimated, it 
was necessary to know the mass of each planet ; and 
though the planets had severally been weighed by 
methods supplied by Newton's ' Principia,' yet the es- 
timate had not then attained the same measure of ac- 
curacy as it has now reached ; nor was it certain that 
there was not (as it has since appeared that there ac- 
tually was) one or more planets beyond Saturn, whose 
attractions might likewise influence the motions of the 
comet. Clairaut, making the best estimate he was 
able, under all these disadvantages, of the disturbing 
influence of the planets, fixed the return of the comet 
to the place of its nearest distance from the sun on the 
fourth of April, 1759. 

In the successive appearances of the comet, subse- 
quently to 1456, it was found to have gradually decreas- 
ed in magnitude and splendor. While in 1456 it 
reached across one third part of the firmament, and 
spread terror over Europe, in 1607, its appearance, 
when observed by Kepler and Longomontanus, was that 
of a star of the first magnitude ; and so trifling was its 
tail that, Kepler himself, when he first saw it, doubted 
whether it had any. In 1682, it excited little attention, 
except among astronomers. Supposing this decrease 
of magnitude and brilliancy to be progressive, Lalande 
entertained serious apprehensions that on its expected 
return it might be so inconsiderable, as to escape the 
observation even of astronomers ; and thus, that this 


splendid example of the power of science, and unan- 
swerable proof of the principle of gravitation, would 
be lost to the world. 

It is not uninteresting to observe the misgivings of 
this distinguished astronomer with respect to the ap- 
pearance of the body, mixed up with his unshaken 
faith in the result of the astronomical inquiry. " We 
cannot doubt," says he, " that it will return ; and even 
if astronomers cannot see it, they will not therefore be 
the less convinced of its presence. They know that 
the faintness of its light, its great distance, and perhaps 
even bad weather, may keep it from our view. But the 
world will find it difficult to believe us ; they will place 
this discovery, which has done so much honor to mod- 
ern philosophy, among the number of chance predic- 
tions. We shall see discussions spring up again in 
colleges, contempt among the ignorant, terror among 
the people ; and seventy-six years will roll away, be- 
fore there will be another opportunity of removing all 

Fortunately for science, the arrival of the expected 
visitor did not take place under such untoward circum- 
stances. As the commencement of the year 1759 ap- 
proached, " astronomers," says Voltaire, " hardly went 
to bed at all." The honor, however, of the first glimpse 
of the stranger was not reserved for the possessors 
of scientific rank, nor for the members of academies 
or universities. On the night of Christmas-day, 1758, 
George Palitzch, of Politz, near Dresden, " a peasant," 
says Sir John Herchel, " by station, an astronomer by 
nature," first saw the comet. 

An astronomer of Leipzic found it soon after ; but, 
with the mean jealousy of a miser, he concealed his 
treasure, while his contemporaries throughout Europe 
were vainly directing their anxious search after it to 
other quarters of the heavens. At this time, Delisle, 
a French astronomer, and his assistant, Messier, who, 
from his unweared assiduity in the pursuit of comets, 
was called the Comet-Hunter, had been constantly 

COMETS. 333 

engaged, for eighteen months, in watching for the re- 
turn of Halley's comet. Messier passed his life in 
search of comets. It is related of him, that when he 
was in expectation of discovering a comet, his wife was 
taken ill and died. While attending on her, being 
withdrawn from his observatory, another astronomer 
anticipated him in the discovery. Messier was in des- 
pair. A friend, visiting him, began to offer some con- 
solation for the recent affliction he had suffered. Mes- 
sier, thinking only of the comet, exclaimed, " I had dis- 
covered twelve : alas, that I should be robbed of the 
thirteenth by Montagne !" and his eyes filled with 
tears. Then, remembering that it was necessary to 
mourn for his wife, whose remains were still in the 
house, he exclaimed, " Ah ! this poor woman !" (ah I 
cette pauvre femme,) and again wept for his comet. 
We can easily imagine how eagerly such an enthusiast 
would watch for Halley's comet ; and we could almost 
wish that it had been his good fortune to be the first 
to announce its arrival ; but, being misled by a chart 
which directed his attention to the wrong part of the 
firmament, a whole month elapsed after its discovery 
by Palitzch, before he enjoyed the delightful spectacle. 
The comet arrived at its perihelion on the thirteenth 
of March, only twenty-three days from the time assign- 
ed by Clairaut. It appeared very round, with a bril- 
liant nucleus, well distinguished from the surrounding 
nebulosity. It had, however, no appearance of a tail. 
It became lost in the sun, as it approached its perihe- 
lion, and emerged again, on the other side of the sun, 
on the first of April. Its exhibiting an appearance, so 
inferior to what it presented on some of its previous re- 
turns, is partly accounted for by its being seen by the 
European astronomers under peculiarly disadvantageous 
circumstances, being almost always within the twilight, 
and in the most unfavorable situations. In the south- 
ern hemisphere, however, the circumstances for observ- 
ing it were more favorable, and there it exhibited a tail 
varying from ten to forty-seven degrees in length,- 


In my next Letter I will give you some particulars 
respecting the late return of Halley's comet. 



" Incensed with indignation, Satan stood 
Unterrifled, and like a comet burned, 
That fires the length of Ophiucus huge 
In the Arctic sky, and from his horrid train 
Shakes pestilence and war." Milton. 

AMONG other great results which have marked the 
history of Halley's comet, it has itself been a criterion 
of the existing state of the mathematical and astronom- 
ical sciences. We have just seen how far the knowl- 
edge of the great laws of physical astronomy, and of 
the higher mathematics, enabled the astronomers of 
1682 and 1759, respectively, to deal with this wonder- 
ful body ; and let us now see what higher advantages 
were possessed by the astronomers of 1835. During 
this last interval of seventy-six years, the science of 
mathematics, in its most profound and refined branch- 
es, has made prodigious advances, more especially in 
its application to the laws of the celestial motions, as 
exemplified in the c Mecanique Celeste' of La Place. 
The methods of investigation have acquired greater 
simplicity, and have likewise become more general and 
comprehensive ; and mechanical science, in the largest 
sense of that term, now embraces in its formularies the 
most complicated motions, and the most minute effects 
of the mutual influences of the various members of our 
system. You will probably find it difficult to compre- 
hend, how such hidden facts can be disclosed by for- 
mularies, consisting of a's and 6's, and x's and i/'s, and 
other algebraic symbols ; nor will it be easy to give 
you a clear idea of this subject, without a more exten- 
sive acquaintance than you have formed with algebraic 
investigations ; but you can easily understand that even 

COMETS. 335 

an equation expressed in numbers may be so changed in 
its form, by adding, subtracting, multiplying and divid- 
ing, as to express some new truth at every transforma- 
tion. Some idea of this may be formed by the sim- 
plest example. Take the following: 3+4=7. This 
equation expresses the fact, that three added to four is 
equal to seven. By multiplying all the terms by 2, we 
obtain a new equation, in which 6+8=14. This ex- 
presses a new truth ; and by varying the form, by sim- 
ilar operations, an indefinite number of separate truths 
may be elicited from the simple fundamental expres- 
sion. I will add another illustration, which involves a 
little more algebra, but not, I think, more than you can 
understand ; or, if it does, you will please pass over it 
to the next paragraph. According to a rule of arith- 
metical progression, the sum of all the terms is equal 
to half the sum of the extremes multiplied into the 
number of terms. Calling the sum of the terms s, the 
first term a, the last h, and the number of terms n, and 
we have \n(a-\-h)=s ; or n(a-\-h)=2s ; or a+A=^ ; 
or a==^ h ; or h 2 ^- a. These are only a few of 
the changes which may be made in the original ex- 
pression, still preserving the equality between the quan- 
tities on the left hand and those on the right ; yet each 
of these transformations expresses a new truth, indi- 
cating distinct and (as might be the case) before un- 
known relations between the several quantities of which 
the whole expression is composed. The last, for exam- 
ple, shows us that the last term in an arithmetical se- 
ries is always equal to twice the sum of the whole se- 
ries divided by the number of terms and diminished by 
the first term. In analytical formularies, as expressions 
of this kind are called, the value of a single unknown 
quantity is sometimes given in a very complicated ex- 
pression, consisting of known quantities ; but before 
we can ascertain their united value, we must reduce 
them, by actually performing all the additions, subtrac- 
tions, multiplications, divisions, raising to powers, and 


extracting roots, which are denoted by the symbols. 
This makes the actual calculations derived from such 
formularies immensely laborious. We have already 
had an instance of this in the calculations made by 
Lalande and Madame Lepaute, from formularies fur- 
nished by Clairaut. 

The analytical formularies, contained in such works 
as La Place's ' Mecanique Celeste,' exhibit to the eye of 
the mathematician a record of all the evolutions of the 
bodies of the solar system in ages past, and of all the 
changes they must undergo in ages to come. Such 
has been the result of the combination of transcendent 
mathematical genius and unexampled labor and perse- 
verance, for the last century. The learned societies 
established in various centres of civilization have more 
especially directed their attention to the advancement 
of physical astronomy, and have stimulated the spirit 
of inquiry by a succession of prizes, offered for the 
solutions of problems arising out of the difficulties 
which were progressively developed by the advance- 
ment of astronomical knowledge. Among these ques- 
tions, the determination of the return of comets, and 
the disturbances which they experience in their course, 
by the action of the planets near which they happen to 
pass, hold a prominent place. In 1826, the French 
Institute offered a prize for the determination of the 
exact time of the return of Halley's comet to its peri- 
helion in 1835. M. Pontecoulant aspired to the honor. 
" After calculations," says he, " of which those alone 
who have engaged in such researches can estimate the 
extent and appreciate the fastidious monotony, I arriv- 
ed at a result which satisfied all the conditions propos- 
ed by the Institute. I determined the perturbations 
of Halley's comet, by taking into account the simulta- 
neous actions of Jupiter, Saturn, Uranus, and the Earth ; 
and I then fixed its return to its perihelion for the sev- 
enth of November." Subsequently to this, however, 
M. Pontecoulant made some further researches, which 
led him to correct the former result ; and he afterwards 

COMETS. 337 

altered the time to November fourteenth. It actually 
came to its perihelion on the sixteenth, within two days 
of the time assigned. 

Nothing can convince us more fully of the complete 
mastery which astronomers have at last acquired over 
these erratic bodies, than to read in the Edinburgh Re- 
view for April, 1835, the paragraph containing the final 
results of all the labors and anticipations of astrono- 
mers, matured as they were, in readiness for the ap- 
proaching visitant, and then to compare the prediction 
with the event, as we saw it fulfilled a few months af- 
terwards. The paragraph was as follows: "On the 
whole, it may be considered as tolerably certain, that 
the comet will become visible in every part of Europe 
about the latter end of August, or beginning of Sep- 
tember, next. It will most probably be distinguishable 
by the naked eye, like a star of the first magnitude, 
but with a duller light than that of a planet, and 
surrounded with a pale nebulosity, which will slightly 
impair its splendor. On the night of the seventh of 
October, the comet will approach the well-known con- 
stellation of the Great Bear ; and between that and the 
eleventh, it will pass directly through the seven con- 
spicuous stars of that constellation, (the Dipper.) Tow- 
ards the end of November, the comet will plunge 
among the rays of the sun, and disappear, and will not 
issue from them, on the other side, until the end of De- 

Let us now see how far the actual appearances cor- 
responded to these predictions. The comet was first 
discovered from the observatory at Rome, on the morn- 
ing of the fifth of August ; by Professor Struve, at Dor- 
pat, on the twentieth ; in England and France, on the 
twenty-third ; and at Yale College, by Professor Loomis 
and myself, on the thirty-first. On the morning of that 
day, between two and three o'clock, in obedience to 
the directions which the great minds that had marked 
out its path among the stars had prescribed, we direct- 
ed Clarke's telescope (a noble instrument, belonging 

29 L. A. 


to Yale College) towards the northeastern quarter of 
the heavens, and lo ! there was the wanderer so long 
foretold, a dim speck of fog on the confines of crea- 
tion. It carne on slowly, from night to night, increas- 
ing constantly in magnitude and brightness, but did not 
become distinctly visible to the naked eye until the 
twenty-second of September. For a month, therefore, 
astronomers enjoyed this interesting spectacle before it 
exhibited itself to the world at large. From this time 
it moved rapidly along the northern sky, until, about 
the tenth of October, it traversed the constellation 
of the Great Bear, passing a little above, instead of 
" through" the seven conspicuous stars constituting the 
Dipper. At this time it had a lengthened train, and 
became, as you doubtless remember, an object of uni- 
versal interest. Early in November, the comet ran 
down to the sun, and was lost in his beams ; but on 
the morning of December thirty-first, I again obtained, 
through Clarke's telescope, a distinct view of it on the 
other side of the sun, a moment before the morning 

This return of Halley's comet was an astronomical 
event of transcendent importance. It was the chroni- 
cler of ages, and carried us, by a few steps, up to the 
origin of time. If a gallant ship, which has sailed 
round the globe, and commanded successively the ad- 
miration of many great cities, diverse in language and 
customs, is invested with a peculiar interest, what in- 
terest must attach to one that has made the circuit 
of the solar system, and fixed the gaze of successive 
worlds ! So intimate, moreover, is the bond which 
binds together all truths in one indissoluble chain, that 
the establishment of one great truth often confirms a 
multitude of others, equally important. Thus the re- 
turn of Halley's comet, in exact conformity with the 
predictions of astronomers, established the truth of all 
those principles by which those predictions were made. 
It afforded most triumphant proof of the doctrine of 
universal gravitation, and of course of the received 

COMETS. 339 

laws of physical astronomy ; it inspired new confidence 
in the power and accuracy of that instrument (the cal- 
culus) by means of which its elements had been inves- 
tigated ; and it proved that the different planets, which 
exerted upon it severally a disturbing force proportion- 
ed to their quantity of matter, had been correctly weigh- 
ed, as in a balance. 

I must now leave this wonderful body to pursue its 
sublime march far beyond the confine? of Uranus, (a 
distance it has long since reached,) and take a hasty 
notice of two other comets, whose periodic returns have 
also been ascertained ; namely, those of Biela and 

Biela's comet has a period of six years and three 
quarters. It has its perihelion near the orbit of the 
earth, and its aphelion a little beyond that of Jupiter. 
Its orbit, therefore, is far less eccentric than that of 
Halley's comet ; (see Frontispiece ;) it neither ap- 
proaches so near the sun, nor departs so far from it, as 
most other known comets : some, indeed, never come 
nearer to the sun than the orbit of Jupiter, while they 
recede to an incomprehensible distance beyond the re- 
motest planet. We might even imagine that they 
would get beyond the limits of the sun's attraction ; 
nor is this impossible, although, according to La Place, 
the solar attraction is sensible throughout a sphere 
whose radius is a hundred millions of times greater 
than the distance of the earth from the sun, or nearly 
ten thousand billions of miles. 

Some months before the expected return of Biela's 
comet, in 1832, it was announced by astronomers, who 
had calculated its path, that it would cross the plane 
of the earth's orbit very near to the earth 5 s path, so 
that, should the earth happen at the time to be at that 
point of her revolution, a collision might take place. 
This announcement excited so much alarm among the 
ignorant classes in France, that it was deemed expedi- 
ent by the French academy, that one of their number 
should prepare and publish an article on the subject, 


with the express view of allaying popular apprehension. 
This task was executed by M. Arago. He admitted 
that the earth would in fact pass so near the point 
where the comet crossed the plane of its orbit, that, 
should they chance to meet there, the earth would be 
enveloped in the nebulous atmosphere of the comet. 
He, however, showed that the earth would not be near 
that point at the same time with the comet, but fifty 
millions of miles from it. 

The comet came at the appointed time, but was so 
exceedingly faint and small, that it was visible only to 
the largest telescopes. In one respect, its diminutive 
size and feeble light enhanced the interest with which 
it was contemplated ; for it was a sublime spectacle to 
see a body, which, as projected on the celestial vault, 
even when magnified a thousand times, seemed but 
a dim speck of fog, still pursuing its way, in obedi- 
ence to the laws of universal gravitation, with the 
same regularity as Jupiter and Saturn. We are apt 
to imagine that a body, consisting of such light mate- 
rials that it can be compared only to the thinnest fog, 
would be dissipated and lost in the boundless regions 
of space ; but so far is this from the truth, that, when 
subjected to the action of the same forces of projection 
and solar attraction, it will move through the void re- 
gions of space, and will describe its own orbit about 
the sun with the same unerring certainty, as the dens- 
est bodies of the system. 

Encke's comet, by its frequent returns, (once in 
three and a third years,) affords peculiar facilities for 
ascertaining the laws of its revolution ; and it has kept 
the appointments made for it with great exactness. On 
its return in 1839, it exhibited to the telescope a glob- 
ular mass of nebulous matter, resembling fog, and 
moved towards its perihelion with great rapidity. It 
makes its entire excursions within the orbit of Jupiter. 

But what has made Encke's comet particularly fa- 
mous, is its having first revealed to us the existence of 
a resisting medium in the planetary spaces. It has 

COMETS. 341 

long been a question, whether the earth and planets 
revolve in a perfect void, or whether a fluid of extreme 
rarity may not be diffused through space. A perfect 
vacuum was deemed most probable, because no such 
effects on the motions of the planets could be detected 
as indicated that they encountered a resisting medium. 
But a feather, or a lock of cotton, propelled with great 
velocity, might render obvious the resistance of a me- 
dium which would not be perceptible in the motions 
of a cannon ball. Accordingly, Encke's comet is 
thought to have plainly suffered a retardation from en- 
countering a resisting medium in the planetary regions. 
The effect of this resistance, from the first discovery of 
the comet to the present time, has been to diminish the 
time of its revolution about two days. Such a resist- 
ance, by destroying a part of the projectile force, would 
cause the comet to approach nearer to the sun, and 
thus to have its periodic time shortened. The ul- 
timate effect of this cause will be to bring the comet 
nearer to the sun, at every revolution, until it finally 
falls into that luminary, although many thousand years 
will be required to produce this catastrophe. It is con- 
ceivable, indeed, that the effects of such a resistance 
may be counteracted by the attraction of one or more 
of the planets, near which it may pass in its successive 
returns to the sun. Still, it is not probable that this 
cause will exactly counterbalance the other ; so that, if 
there is such an elastic medium diffused through the 
planetary regions, it must follow that, in the lapse of 
ages, every comet will fall into the sun. Newton con- 
jectured that this would be the case, although he did 
not found his opinion upon the existence of such a re- 
sisting medium as is now detected. To such an opin- 
ion he adhered to the end of life. At the age of 
eighty-three, in a conversation with his nephew, he ex- 
pressed himself thus : " I cannot say when the comet 
of 1680 will fall into the sun ; possibly after five or six 
revolutions ; but whenever that time shall arrive, the 
heat of the sun will be raised by it to such a point, that 



our globe will be burned, and all the animals upon it 
will perish." 

Of the physical nature of comets little is understood. 
The greater part of them are evidently mere masses of 
vapor, since they permit very small stars to be seen 
through them. In September, 1832, Sir John Her- 
schel, when observing Biela's comet, saw that body pass 
directly between his eye and a small cluster of minute 
telescopic stars of the sixteenth or seventeenth magni- 
tude. This little constellation occupied a space in the 
heavens, the breadth of which was not the twentieth 
part of that of the moon ; yet the whole of the cluster 
was distinctly visible through the comet. "A more 
striking proof," says Sir John Herschel, " could not 
have been afforded, of the extreme transparency of the 
matter of which this comet consists. The most trifling 
fog would have entirely effaced this group of stars, yet. 
they continued visible through a thickness of the comet 
which, calculating on its distance and apparent diame- 
ter, must have exceeded fifty thousand miles, at least 
towards its central parts." From this and similar ob- 
servations, it is inferred, that the nebulous matter of 
comets is vastly more rare than that of the air we 
breathe, and hence, that, were more or less of it to be 
mingled with the earth's atmosphere, it would not be 
perceived, although it might possibly render the air tin- 
wholesome for respiration. M. Arago, however, is of 
the opinion, that some comets, at least, have a solid 
nucleus. It is difficult, on any other supposition, to 
account for the strong light which some of them have 
exhibited, a light sufficiently intense to render them 
visible in the day-time, during the presence of the sun. 
The intense heat to which comets are subject, in ap- 
proaching so near the sun as some of them do, is alleged 
as a sufficient reason for the great expansion of the 
thin vapory atmospheres which form their tails ; and the 
inconceivable cold to which they are subject, in receding 
to such a distance from the sun, is supposed to account 
for the condensation of the same matter until it returns 

COMETS. 343 

to its original dimensions. Thus the great comet of 
1680, at its perihelion, approached within one hun- 
dred and forty-six thousand miles of the surface of 
the sun, a distance of only one sixth part of the sun's 
diameter. The heat which it must have received was 
estimated to be equal to twenty-eight thousand times 
that which the earth receives in the same time, and 
two thousand times hotter than red-hot iron. This 
temperature would be sufficient to volatilize the most 
obdurate substances, and to expand the vapor to vast 
dimensions ; and the opposite effects of the extreme 
cold to which it would be subject in the regions remote 
from the sun would be adequate to condense it into its 
former volume. This explanation, however, does not 
account for the direction of the tail, extending, as it 
usually does, only in a line opposite to the sun. Some 
writers, therefore, suppose that the nebulous matter of 
the comet, after being expanded to such a volume that 
the particles are no longer attracted to the nucleus, un- 
less by the slightest conceivable force, are carried off 
in a direction from the sun, by the impulse of the 
solar rays themselves. But to assign such a power to 
the sun's rays, while they have never been proved to 
have any momentum, is unphilosophical ; and we are 
compelled to place the phenomena of comets' tails 
among the points of astronomy yet to be explained. 

Since comets which approach very near the sun, like 
the comet of 1680, cross the orbits of all the planets, 
the possibility that one of them may strike the earth has 
frequently been suggested. Still it may quiet our ap- 
prehensions on this subject, to reflect on the vast am- 
plitude of the planetary spaces, in which these bodies 
are not crowded together, as we see them erroneously 
represented in orreries and diagrams, but are sparsely 
scattered at immense distances from each other. They 
are like insects flying, singly, in the expanse of heaven. 
If a comet's tail lay with its axis in the plane of the 
ecliptic when it was near the sun, we can imagine 
that the tail might sweep over the earth ; but the 


tail may be situated at any angle with the ecliptic, 
as well as in the same plane with it, and the chances 
that it will not be in the same plane are almost infinite. 
It is also extremely improbable that a comet will cross 
the plane of the ecliptic precisely at the earth's path in 
that plane, since it may as probably cross it at any oth- 
er point nearer or more remote from the sun. A French 
writer of some eminence (Du Sejour) has discussed 
this subject with ability, and arrived at the following 
conclusions : That of all the comets whose paths had 
been ascertained, none could pass nearer to the earth 
than about twice the moon's distance ; and that none 
ever did pass nearer to the earth than nine times the 
moon's distance. The comet of 1770, already men- 
tioned, which became entangled among the satellites 
of Jupiter, came within this limit. Some have taken 
alarm at the idea that a comet, by approaching very 
near to the earth, might raise so high a tide, as to en- 
danger the safety of maritime countries especially : but 
this writer shows, that the comet could not possibly re- 
main more than two hours so near the earth as a fourth 
part of the moon's distance ; and it could not remain 
even so long, unless it passed the earth under very pe- 
culiar circumstances. For example, if its orbit were 
nearly perpendicular to that of the earth, it could not 
remain more than half an hour in such a position. Un- 
der such circumstances, the production of a tide would 
be impossible. Eleven hours, at least, would be neces- 
sary to enable a comet to produce an effect on the wa- 
ters of the earth, from which the injurious effects so 
much dreaded would follow. The final conclusion at 
which he arrives is, that although, in strict geometrical 
rigor, it is not physically impossible that a comet should 
encounter the earth, yet the probability of such an event 
is absolutely nothing. 

M. Arago, also, has investigated the probability of 
such a collision on the mathematical doctrine of chan- 
ces, and remarks as follows : " Suppose, now, a comet, 
of which we know nothing but that, at its perihelion, it 

COMETS. 345 

will be nearer the sun than we are, and that its diame- 
ter is equal to one fourth that of the earth ; the doctrine 
of chances shows that, out of two hundred and eighty- 
one millions of cases, there is but one against us ; but 
one, in which the two bodies could meet." 

La Place has assigned the consequences that would 
result from a direct collision between the earth and a 
comet. " It is easy," says he, " to represent the effects 
of the shock produced by the earth's encountering a 
comet. The axis and the motion of rotation changed ; 
the waters abandoning their former position to precipi- 
tate themselves towards the new equator ; a great part 
of men and animals whelmed in a universal deluge, or 
destroyed by the violent shock imparted to the terres- 
trial globe ; entire species annihilated ; all the monu- 
ments of human industry overthrown ; such are the 
disasters which the shock of a comet would necessarily 
produce." La Place, nevertheless, expresses a decid- 
ed opinion that the orbits of the planets have never yet 
been disturbed by the influence of comets. Comets, 
moreover, have been, and are still to some degree, 
supposed to exercise much influence in the affairs of 
this world, affecting the weather, the crops, the public 
health, and a great variety of atmospheric commotions. 
Even Halley, finding that his comet must have been 
near the earth at the time of the Deluge, suggested the 
possibility that the comet caused that event, an idea 
which was taken up by Whiston, and formed into a 
regular theory. In Gregory's Astronomy, an able work, 
published at Oxford in 1702, the author remarks, that 
among all nations and in all ages, it has been observed, 
that the appearance of a comet has always been fol- 
lowed by great calamities ; and he adds, " it does not 
become philosophers lightly to set down these things as 
fables." Among the various things ascribed to comets 
by a late English writer, are hot and cold seasons, tem- 
pests, hurricanes, violent hail-storms, great falls of snow, 
heavy rains, inundations, droughts, famines, thick fogs, 
flies, grasshoppers, plague, dysentery, contagious dis- 


eases among animals, sickness among cats, volcanic 
eruptions, and meteors, or shooting stars. These no- 
tions are too ridiculous to require a distinct refutation ; 
and I will only add, that we have no evidence that 
comets have hitherto ever exercised the least influence 
upon the affairs of this world ; and we still remain in 
darkness, with respect to their physical nature, and the 
purposes for which they were created. 



"Oft shall them see, ere brooding storms arise, 
Star after star glide headlong down the skies, 
And, where they shot, long trails of lingering light 
Sweep far behind, and gild the shades of night." Virgil. 

FEW subjects of astronomy have excited a more 
general interest, for several years past, than those ex- 
traordinary exhibitions of shooting stars, which have ac- 
quired the name of meteoric showers. My reason for 
introducing the subject to your notice, in this place, is, 
that these small bodies are, as I believe, derived from 
nebulous or cometaf-y bodies, which belong to the solar 
system, and which, therefore, ought to be considered, 
before we take our leave of this department of creation, 
and naturally come next in order to comets. 

The attention of astronomers was particularly direct- 
ed to this subject by the extraordinary shower of me- 
teors which occurred on the morning of the thirteenth 
of November, 1833. I had the good fortune to wit- 
ness these grand celestial fire-works, and felt, a strong 
desire that a phenomenon, which, as it afterwards ap- 
peared, was confined chiefly to North America, should 
here command that diligent inquiry into its causes, 
which so sublime a spectacle might justly claim. 

As I think you were not so happy as to witness this 
magnificent display, I will endeavor to give you some 
faint idea of it, as it appeared to me a little before day- 


break. Imagine a constant succession of fire-balls, re- 
sembling sky-rockets, radiating in all directions from a 
point in the heavens a few degrees southeast of the ze- 
nith, and following the arch of the sky towards the ho- 
rizon. They commenced their progress at different 
distances from the radiating point ; but their directions 
were uniformly such, that the lines they described, if 
produced upwards, would all have met in the same part 
of the heavens. Around this point, or imaginary ra- 
diant, was a circular space of several degrees, within 
which no meteors were observed. The balls, as they 
travelled down the vault, usually left after them a vivid 
streak of light ; and, just before they disappeared, ex- 
ploded, or suddenly resolved themselves into smoke. 
No report of any kind was observed, although we lis- 
tened attentively. 

Beside the foregoing distinct concretions, or individ- 
ual bodies, the atmosphere exhibited phosphoric lines, 
following in the train of minute points, that shot off in 
the greatest abundance in a northwesterly direction. 
These did not so fully copy the figure of the sky, but 
moved in paths more nearly rectilinear, and appeared 
to be much nearer the spectator than the fire-balls. 
The light of their trains was also of a paler hue, not 
unlike that produced by writing with a stick of phos- 
phorus on the walls of a dark room. The number of 
these luminous trains increased and diminished alter- 
nately, now and then crossing the field of view, like 
snow drifted before the wind, although, in fact, their 
course was towards the wind. 

From these two varieties, we were presented with 
meteors of various sizes and degrees of splendor : some 
were mere points, while others were larger and bright- 
er than Jupiter or Venus ; and one, seen by a credible 
witness, at an earlier hour, was judged to be nearly as 
large as the moon. The flashes of light, although less 
intense than lightning, were so bright, as to awaken 
people in their beds. One ball that shot off in the 
northwest direction, and exploded a little northward of 


the star Capella, left, just behind the place of explosion, 
a phosphorescent train of peculiar beauty. This train 
was at first nearly straight, but it shortly began to con- 
tract in length, to dilate in breadth, and to assume the 
figure of a serpent drawing itself up, until it appeared 
like a small luminous cloud of vapor. This cloud was 
borne eastward, (by the wind, as was supposed, which 
was blowing gently in that direction,) opposite to the 
direction in which the meteor itself had moved, remain- 
ing in sight several minutes. The point from which 
the meteors seemed to radiate kept a fixed position 
among the stars, being constantly near a star in Leo, 
called Gamma Leonis. 

Such is a brief description of this grand and beauti- 
ful display, as I saw it at New Haven. The newspa- 
pers shortly brought^us intelligence of similar appear- 
ances in all parts of the United States, and many mi- 
nute descriptions were published by various observers ; 
from which it appeared, that the exhibition had been 
marked by very nearly the same characteristics wher- 
ever it had been seen. Probably no celestial phenom- 
enon has ever occurred in this country, since its first 
settlement, which was viewed with so much admiration 
and delight by one class of spectators, or with so much 
astonishment and fear by another class. It striking- 
ly evinced the progress of knowledge and civilization, 
that the latter class was comparatively so small, although 
it afforded some few examples of the dismay with which, 
in barbarous ages of the world, such spectacles as this 
were wont to be regarded. One or two instances were 
reported, of persons who died with terror ; many oth- 
ers thought the last great day had come ; and the un- 
tutored black population of the South gave expression 
to their fears in cries and shrieks. 

After collecting and collating the accounts given in 
all the periodicals of the country, and also in numerous 
letters addressed either to my scientific friends or to my- 
self, the following appeared to be the leading facts at- 
tending the phenomenon. The shower pervaded near- 


ly the whole of North America, having appeared in 
nearly equal splendor from the British possessions on 
the north to the West-India Islands and Mexico on 
the south, and from sixty-one degrees of longitude east 
of the American coast, quite to the Pacific Ocean on 
the west. Throughout this immense region, the dura- 
tion was nearly the same. The meteors began to at- 
tract attention by their unusual frequency and brillian- 
cy, from nine to twelve o'clock in the evening ; were 
most striking in their appearance from two to five ; ar- 
rived at their maximum, in many places, about four 
o'clock ; and continued until rendered invisible by the 
light of day. The meteors moved either in right lines, 
or in such apparent curves, as, upon optical principles, 
can be resolved into right lines. Their general tenden- 
cy was towards the northwest, although, by the effect 
of perspective, they appeared to move in various direc- 

Such were the leading phenomena of the great me- 
teoric shower of November 13, 1833. For a fuller de- 
tail of the facts, as well as of the reasonings that were 
built on them, I must beg leave to refer you to some 
papers of mine in the twenty-fifth and twenty-sixth 
volumes of the American Journal of Science. 

Soon after this remarkable occurrence, it was ascer- 
tained that a similar meteoric shower had appeared in 
1799, and, what was remarkable, almost at exactly 
the same time of year, namely, on the morning of the 
twelfth of November ; and we were again surprised as 
well as delighted, at receiving successive accounts from 
different parts of the world of the phenomenon, as hav- 
ing occurred on the morning of the same thirteenth of 
November, in 1830, 1831, and 1832. Hence this was 
evidently an event independent of the casual changes 
of the atmosphere ; for, having a periodical return, it 
was undoubtedly to be referred to astronomical causes, 
and its recurrence, at a certain definite period of the 
year, plainly indicated some relation to the revolution 
of the earth around the sun.- It remained, however, to 
30 L. A. 


develope the nature of this relation, by investigating', 
if possible, the origin of the meteors. The views to 
which I was led on this subject suggested the probabil- 
ity that the same phenomenon would recur on the cor- 
responding seasons of the year, for at least several years 
afterwards ; and such proved to be the fact, although 
the appearances, at every succeeding return, were less 
and less striking, until 1839, when, so far as I have 
heard, they ceased altogether. 

Mean-while, two other distinct periods of meteoric 
showers have, as already intimated, been determined ; 
namely, about the ninth of August, and seventh of De- 
cember. The facts relative to the history of these 
periods have been collected with great industry by Mr. 
Edward C. Herrick ; and several of the most ingenious 
and most useful conclusions, respecting the laws that 
regulate these singular exhibitions, have been deduced 
by Professor Twining. Several of the most distin- 
guished astronomers of the Old World, also, have en- 
gaged in these investigations with great zeal, as Messrs. 
Arago and Biot, of Paris ; Doctor Olbers, of Bremen ; 
M. Wartmann, of Geneva ; and M. Quetelet, of Brussels. 

But you will be desirous to learn what are the con- 
clusions which have been drawn respecting these new 
and extraordinary phenomena of the heavens. As 
the inferences to which I was led, as explained in 
the twenty-sixth volume of the ' American Journal of 
Science,' have, at least in their most important points, 
been sanctioned by astronomers of the highest respec- 
tability, I will venture to give you a brief abstract of 
them, with such modifications as the progress of inves- 
tigation since that period has rendered necessary. 

The principal questions involved in the inquiry were 
the following : Was the origin of the meteors within 
the atmosphere, or beyond it ? What was the height 
of the place above the surface of the earth ? By what 
force were the meteors drawn or impelled towards the 
earth ? In what directions did they move ? With 
what velocity ? What was the cause of their light and 


heat ? Of what size were the larger varieties ? At what 
height above the earth did they disappear ? What was 
the nature of the luminous trains which sometimes re- 
mained behind ? What sort of bodies were the me- 
teors themselves ; of what kind of matter constituted ; 
and in what manner did they exist before they fell to 
the earth 1 Finally, what relations did the source from 
which they emanated sustain to our earth ? 

In the first place, the meteors had their origin be- 
yond the limits of our atmosphere. We know wheth- 
er a given appearance in the sky is within the atmos- 
phere or beyond it, by this circumstance: all bodies 
near the earth, including the atmosphere itself, have a 
common motion with the earth around its axis from west 
to east. When we see a celestial object moving regu- 
larly from west to east, at the same rate as the earth 
moves, leaving the stars behind, we know it is near the 
earth, and partakes, in common with the atmosphere, 
of its diurnal rotation : but when the earth leaves the 
object behind ; or, in other words, when the object 
moves westward along with the stars, then we know 
that it is so distant as not to participate in the diurnal 
revolution of the earth, and of course to be beyond the 
atmosphere. The source from which the meteors em- 
anated thus kept pace with the stars, and hence was 
beyond the atmosphere. 

In the second place, the height of the place whence 
the meteors proceeded was very great, but it has not 
yet been accurately determined. Regarding the body 
whence the meteors emanated after the similitude of a 
cloud, it seemed possible to obtain its height in the 
same manner as we measure the height of a cloud, or 
indeed the height of the moon. Although we could 
not see the body itself, yet the part of the heavens 
whence the meteors came would indicate its position. 
This point we called the radiant; and the question 
was, whether the radiant was projected by distant ob- 
servers on different parts of the sky ; that is, whether 
it had any parallax. I took much pains to ascertain 
the truth of this matter, by corresponding with various 


observers in different parts of the United States, who 
had accurately noted the position of the radiant among 
the fixed stars, and supposed I had obtained such ma- 
terials as would enable us to determine the parallax, at 
least approximately ; although such discordances exist- 
ed in the evidence as reasonably to create some distrust 
of its validity. Putting together, however, the best ma- 
terials I could obtain, I made the height of the radiant 
above the surface of the earth twenty-two hundred and 
thirty-eight miles. When, however, I afterwards ob- 
tained, as I supposed, some insight into the celestial 
origin of the meteors, I at once saw that the meteoric 
body must be much further off than this distance ; and 
my present impression is, that we have not the means 
of determining what its height really is. We may safe- 
ly place it at many thousand miles. 

In the third place, with respect to the force by which 
the meteors were drawn or impelled towards the earth, 
my first impression was, that they fell merely by the 
force of gravity ; but the velocity which, on careful in- 
vestigation by Professor Twining and others, has been 
ascribed to them, is greater than can possibly result 
from gravity, since a body can never acquire, by grav- 
ity alone, a velocity greater than about seven miles 
per second. Some other cause, beside gravity, must 
therefore act, in order to give the meteors so great an 
apparent velocity. 

In the fourth place, the meteors fell towards the 
earth in straight lines, and in directions which, with- 
in considerable distances, were nearly parallel tvith 
each other. The courses are inferred to have been in 
straight lines, because no others could have appeared 
to spectators in different situations to have described 
arcs of great circles. In order to be projected into 
the arc of a great circle, the line of descent must be in 
a plane passing through the eye of the spectator ; and 
the intersection of such planes, passing through the eyes 
of different spectators, must be straight lines. The 
lines of direction are inferred to have been parallel, on 
account of their apparent radiation from one point, that 



being the vanishing point of parallel lines. This may 
appear to you a little paradoxical, to infer that lines are 
parallel, because they diverge from one and the same 
point ; but it is a well-known principle of perspective, 
that parallel lines, when continued to a great distance 
from the eye, appear to converge towards the remoter 
end. You may observe this in two long rows of trees, 
or of street lamps. 

Some idea of the manner in which the meteors fell, 
and of the reason of their apparent radiation from a 
common point, may be gathered from the annexed di- 
agram. Let ABC, Fig. 69, represent the vault of the 

Fig. 69. 



sky, the centre of which, D, being the place of the spec- 
tator. Let 1, 2, 3, &c., represent parallel lines direct- 
ed towards the earth, A luminous body descending 
through 1' 1, coinciding with the line D E, coincident 
with the axis of vision, (or the line drawn from the me- 
teoric body to the eye,) would appear stationary all 
the while at 1', because distant bodies always appear 
stationary when they are moving either directly towards 
us or directly from us. A body descending through 
2 2, would seem to describe the short arc 2' 2', ap- 
pearing to move on the concave of the sky between the 
lines drawn from the eye to the two extremities of its 
line of motion ; and, for a similar reason, a body de- 
scending through 3 3, would appear to describe the 
larger arc 3' 3'. Hence, those meteors which fell near- 
er to the axis of vision, would describe shorter arcs, and 
move slower, while those which were further from the 
axis and nearer ;tfo 'horizon would appear to describe 
longer arcs, anc^ta move with greater velocity ; the me- 
teors would .allj,seem to radiate from a common centre, 
namely, the point where the axis of vision met the ce- 
lestial vault; and if any meteor chanced to move di- 
rectly in the line of vision, it would be seen as a lumi- 
nous body, stationary, for a few seconds, at the centre 
of radiation. To see how exactly the facts, as observ- 
ed, corresponded to these inferences, derived from the 
supposition that the meteors moved in parallel lines, 
take the following description, as given immediately after 
the occurrence, by Professor Twining. " In the vicin- 
ity of the radiant point, a few star-like bodies were ob- 
served, possessing very little motion, and leaving very 
little length of trace. Further off, the motions were more 
rapid and the traces longer ; and most rapid of all, and 
longest in their traces, were those which originated but 
a few degrees above the horizon, and descended down 
to it." 

In the fifth place, had the meteors come from a point 
twenty-two hundred and thirty-eight miles from the 
earth, and derived their apparent velocity from gravity 


alone, then it would be found, by a very easy calcula- 
tion, that their actual velocity was about four miles per 
second ; but, as already intimated, the velocity observ- 
ed was estimated much greater than could be account- 
ed for on these principles ; not less, indeed, than four- 
teen miles per second, and, in some instances, much 
greater even than this. The motion of the earth in its 
orbit is about nineteen miles per second ; and the most 
reasonable supposition we can make, at present, to ac- 
count for the great velocity of the meteors, is, that they 
derived a relative motion from the earth's passing rap- 
idly by them, a supposition which is countenanced by 
the fact that they generally tended westward contrary 
to the earth's motion in its orbit. 

In the sixth place, the meteors consisted of com- 
bustible matter, and took fire, and were consumed, in 
traversing the atmosphere. That these bodies under- 
went combustion, we had the direct evidence of the 
senses, inasmuch as we saw them burn. That they 
took fire in the atmosphere, was inferred from the fact 
that they were not luminous in their original situations 
in space, otherwise, we should have seen the body from 
which they emanated ; and had they been luminous 
before reaching the atmosphere, we should have seen 
them for a much longer period than they were in sight, 
as they must have occupied a considerable time in de- 
scending towards the earth from so great a distance, 
even at the rapid rate at which they travelled. The 
immediate consequence of the prodigious velocity with 
which the meteors fell into the atmosphere must be a 
powerful condensation of the air before them, retarding 
their progress, and producing, by a sudden compression 
of the air, a great evolution of heat. There is a little 
instrument called the air-match, consisting of a piston 
and cylinder, like a syringe, in which we strike a light 
by suddenly forcing down the piston upon the air be- 
low. As the air cannot escape, it is suddenly com- 
pressed, and gives a spark sufficient to light a piece of 
tinder at the bottom of the cylinder. Indeed, it is a well- 


known fact, that, whenever air is suddenly and forci- 
bly compressed, heat is elicited ; and, if by such a com- 
pression as may be given by the hand in the air-match, 
heat is evolved sufficient to fire tinder, what must be 
the heat evolved by the motion of a large body in the 
atmosphere, with a velocity so immense. It is com- 
mon to resort to electricity as the agent which produces 
the heat and light of shooting stars ; but even were elec- 
tricity competent to produce this effect, its presence, 
in the case before us, is not proved ; and its agency 
is unnecessary, since so swift a motion of the meteors 
themselves, suddenly condensing the air before them, 
is both a known and adequate cause of an intense light 
and heat. A combustible body falling into the atmos- 
phere, under such circumstances, would become speedi- 
ly ignited, but could not burn freely, until it became 
enveloped in air of greater density ; but, on reaching 
the lower portions of the atmosphere, it would burn 
with great rapidity. 

In the seventh place, some of the larger meteors 
must have been bodies of great size. According to 
the testimony of various individuals, in different parts 
of the United States, a few fire-balls appeared as large 
as the full moon. Dr. Smith, (then of North Carolina, 
but since surgeon-general of the Texian army,) who 
was travelling all night on professional business, de- 
scribes one which he saw in the following terms : " In 
size it appeared somewhat larger than the full moon ris- 
ing. I was startled by the splendid light in which the 
surrounding scene was exhibited, rendering even small 
objects quite visible ; but I heard no noise, although 
every sense seemed to be suddenly aroused, in sympa- 
thy with the violent impression on the sight." This 
description implies not only that the body was very 
large, but that it was at a considerable distance from 
the spectator. Its actual size will depend upon the dis- 
tance ; for, as it appeared under the same angle as the 
moon, its diameter will bear the same ratio to the 
moon's, as its distance bears to the moon's distance. 


We could, therefore, easily ascertain how large it was, 
provided we could find how far it was from the observ- 
er. If it was one hundred and ten miles distant, its 
diameter was one mile, and in the same proportion for 
a greater or less distance ; and, if only at the distance 
of one mile, its diameter was forty-eight feet. For a 
moderate estimate, we will suppose it to have been 
twenty-two miles off; then its diameter was eleven 
hundred and fifty-six feet. Upon every view of the 
case, therefore, it must be admitted, that these were 
bodies of great size, compared with other objects which 
traverse the atmosphere. We may further infer the 
great magnitude of some of the meteors, from the di- 
mensions of the trains, or clouds, which resulted from 
their destruction. These often extended over several 
degrees, and at length were borne along in the direc- 
tion of the wind, exactly in the manner of a small 

It was an interesting problem to ascertain, if possible, 
the height above the earth at which these fire-balls ex- 
ploded, or resolved themselves into a cloud of smoke. 
This would be an easy task, provided we could be cer- 
tain that two or more distant observers could be sure 
that both saw the same meteor ; for as each would re- 
fer the place of explosion, or the position of the cloud 
that resulted from it, to a different point of the sky, a 
parallax would thus be obtained, from which the height 
might be determined. The large meteor which is men- 
tioned in my account of the shower, (see page 348,) 
as having exploded near the star Capella, was so pecu- 
liar in its appearance, and in the form and motions of 
the small cloud which resulted from its combustion, 
that it was noticed and distinguished by a number of 
observers in distant parts of the country. All described 
the meteor as exhibiting, substantially, the same pecu- 
liarities of appearance; all agreed very nearly in the 
time of its occurrence ; and, on drawing lines, to rep- 
resent the course and direction of the place where it 
exploded to the view of each of the observers respec- 


tively, these lines met in nearly one and the same point, 
and that was over the place where it was seen in the 
zenith. Little doubt, therefore, could remain, that all 
saw the same body ; and on ascertaining, from a com- 
parison of their observations, the amount of parallax, 
and thence deducing its height, a task which was ably 
executed by Professor Twining, the following results 
were obtained : that this meteor, and probably all the 
meteors, entered the atmosphere with a velocity not 
less, but perhaps greater, than fourteen miles in a sec- 
ond ; that they became luminous many miles from the 
earth, in this case, over eighty miles ; and became 
extinct high above the surface, in this case, nearly 
thirty miles. 

In the eighth place, the meteors were combustible 
bodies, and were constituted of light and transpa- 
rent materials. The fact that they burned is sufficient 
proof that they belonged to the class of combustible 
bodies ; and they must have been composed of very 
light materials, otherwise their momentum would have 
been sufficient to enable them to make their way through 
the atmosphere to the surface of the earth. To com- 
pare great things with small, we may liken them to a 
wad discharged from a piece of artillery, its velocity 
being supposed to be increased (as it may be) to such 
a degree, that it shall take fire as it moves through the 
air. Although it would force its way to a great dis- 
tance from the gun, yet, if not consumed too soon, it 
would at length be stopped by the resistance of the air. 
Although it is supposed that the meteors did in fact 
slightly disturb the atmospheric equilibrium, yet, had 
they been constituted of dense matter, like meteoric 
stones, they would doubtless have disturbed it vastly 
more. Their own momentum would be lost only as it 
was imparted to the air ; and had such a number of 
bodies, some of them quite large, perhaps a mile in 
diameter, and entering the atmosphere with a velocity 
more than forty times the greatest velocity of a cannon 
ball, had they been composed of dense, ponderous 


matter, we should have had appalling evidence of this 
fact, not only in the violent winds which they would 
have produced in the atmosphere, but in the calamities 
they would have occasioned on the surface of the 
earth. The meteors were transparent bodies ; other- 
wise, we cannot conceive why the body from which 
they emanated was not distinctly visible, at least by re- 
flecting the light of the sun. If only the meteors which 
were known to fall towards the earth had been collect- 
ed and restored to their original connexion in space, 
they would have composed a body of great extent ; 
and we cannot imagine a body of such dimensions, 
under such circumstances, which would not be visible, 
unless formed of highly transparent materials. By 
these unavoidable inferences respecting the kind of 
matter of which the meteors were composed, we are 
unexpectedly led to recognise a body bearing, in its 
constitution, a strong analogy to comets, which are 
also composed of exceedingly light and transparent, 
and, as there is much reason to believe, of combustible 

We now arrive at the final inquiry, what relations 
did the body which afforded the meteoric shower sus- 
tain to the earth ? Was it of the nature of a satellite, 
or terrestrial comet, that revolves around the earth as 
its centre of motion ? Was it a collection of nebulous, 
or cometary matter, which the earth encountered in its 
annual progress ? or was it a comet, which chanced at 
this time to be pursuing its path along with the earth, 
around their common centre of motion ? It could not 
have been of the nature of a satellite to the earth, (or 
one of those bodies which are held by some to afford 
the meteoric stones, which sometimes fall to the earth 
from huge meteors that traverse the atmosphere,) be- 
cause it remained so long stationary with respect to the 
earth. A body so near the earth as meteors of this 
class are known to be, could not remain apparently sta- 
tionary among the stars for a moment; whereas the 
body in question occupied the same position, with 


hardly any perceptible variation, for at least two hours. 
Nor can we suppose that the earth, in its annual prog- 
ress, came into the vicinity of a nebula, which was 
either stationary, or wandering lawless through space. 
Such a collection of matter could not remain stationary 
within the solar system, in an insulated state, for, if not 
prevented by a motion of its own, or by the attraction 
of some nearer body, it would have proceeded directly 
towards the sun ; and had it been in motion in any 
other direction than that in which the earth was mov- 
ing, it would soon have been separated from the earth ; 
since, during the eight hours, while the meteoric show- 
er was visible, the earth moved in its orbit through the 
space of nearly five hundred and fifty thousand miles. 

The foregoing considerations conduct us to the fol- 
lowing train of reasoning. First, if all the meteors 
which fell on the morning of November 13, 1833, had 
been collected and restored to their original connexion 
in space, they would of themselves have constituted a 
nebulous body of great extent ; but we have reason to 
suppose that they, in fact, composed but a small part 
of the mass from which they emanated, since, after the 
loss of so much matter as proceeded from it in the 
great meteoric shower of 1799, and in the several rep- 
etitions of it that preceded the year 1833, it was still 
capable of affording so copious a shower on that year ; 
and similar showers, more limited in extent, were re- 
peated for at least five years afterwards. We are 
therefore to regard the part that descended only as the 
extreme portions of a body or collection of meteors, 
of unknown extent, existing in the planetary spaces. 

Secondly, since the earth fell in with this body in 
the same part of its orbit, for several years in succes- 
sion, it must either have remained there while the earth 
was performing its whole revolution around the sun, or 
it must itself have had a revolution, as well as the earth. 
But I have already shown that it could not have re- 
mained stationary in that part of space ; therefore, it 
must have had a revolution around the sun. 


Thirdly, its period of revolution must have either 
been greater than the earth's, equal to it, or less. It 
could not have been greater, for then the two bodies 
could not have been together again at the end of the 
year, since the meteoric body would not have completed 
its revolution in a year. Its period might obviously be 
the same as the earth's, for then they might easily come 
together again after one revolution of each ; although 
their orbits might differ so much in shape as to prevent 
their being together at any intermediate point. But 
the period of the body might also be less than that of 
the earth, provided it were some aliquot part of a year, 
so as to revolve just twice, or three times, for example, 
while the earth revolves once. Let us suppose that 
the period is one third of a year. Then, since we 
have given the periodic times of the two bodies, and 
the major axis of the orbit of one of them, namely, of 
the earth, we can, by Kepler's law, find the major axis 
of the other orbit ; for the square of the earth's peri- 
odic time I 2 is to the square of the body's time (|) 2 
as the cube of the major axis of the earth's orbit is to 
the cube of the major axis of the orbit in question. 
Now, the three first terms of this proportion are known, 
and consequently, it is only to solve a case in the sim- 
ple rule of three, to find the term required. On mak- 
ing the calculation, it is found, that the supposition of 
a periodic time oNmly one third of a year gives an or- 
bit of insufficient length ; the whole major axis would 
not reach from the sun to the earth ; and consequently, 
a body revolving in it could never come near to the 
earth. On making trial of six months, we obtain an or- 
bit which satisfies the conditions, being such as is rep- 
resented by the diagram on page 362, Fig. 69', where 
the outer circle denotes the earth's orbit, the sun being 
in the centre, and the inner ellipse denotes the path of 
the meteoric body. The two bodies are together at 
the top of the figure, being the place of the meteoric 
body's aphelion on the thirteenth of November, and 
the figures 10, 20, &c., denote the relative positions 
31 L. A. 


Fig. 69'. 

of the earth and the body for every ten days, for a period 
of six months, in which time the body would have return- 
ed to its aphelion. 

Such would be the relation of the body that af- 
fords the meteoric shower of November, provided its 
revolution is accomplished in six months ; but it is still 
somewhat uncertain whether the period be half a year 
or a year ; it must be one or the other. 

If we inquire, now, why the meteors always appear to 
radiate from a point in the constellation Leo, recollect- 
ing that this is the point to which the body is projected 


among the stars, the answer is, that this is the very 
point towards which the earth is moving in her orbit 
at that time ; so that if, as we have proved, the earth 
passed through or near a nebulous body on the thir- 
teenth of November, that body must necessarily have 
been projected into the constellation Leo, else it could 
not have lain directly in her path. I consider it there- 
fore as established by satisfactory proof, that the me- 
teors of November thirteenth emanate from a nebulous 
or cometary body, revolving around the sun, and com- 
ing so near the earth at that time that the earth passes 
through its skirts, or extreme portions, and thus attracts 
to itself some portions of its matter, giving to the 
meteors a greater velocity than could be imparted by 
gravity alone, in consequence of passing rapidly by 

All these conclusions were made out by a process of 
reasoning strictly inductive, without supposing that the 
meteoric body itself had ever been seen. But there 
are some reasons for believing that we do actually see 
it, and that it is no other than that mysterious appear- 
ance long known under the name of the zodiacal light. 
This is a faint light, which at certain seasons of the year 
appears in the west after evening twilight, and at cer- 
tain other seasons appears in the east before the dawn, 
following or preceding the track of the sun in a trian- 
gular figure, with its broad base next to the sun, and 
its vertex reaching to a greater or less distance, some- 
times more than ninety degrees from that luminary. 
You may obtain a good view of it in February or March, 
in the west, or in October, in the morning sky. The 
various changes which this light undergoes at different 
seasons of the year are such as to render it probable, 
to my mind, that this is the very body which affords 
the meteoric showers ; its extremity coming, in Novem- 
ber, within the sphere of the earth's attraction. But, 
as the arguments for the existence of a body in the 
planetary regions, which affords these showers, were 
drawn without the least reference to the zodiacal light, 


and are good, should it finally be proved that this light 
has no connexion with them, I will not occupy your 
attention with the discussion of this point, to the ex- 
clusion of topics which will probably interest you more. 
It is perhaps most probable, that the meteoric show- 
ers of August and December emanate from the same 
body. I know of nothing repugnant to this conclusion, 
although it has not yet been distinctly made out. Had 
the periods of the earth and of the meteoric body been 
so adjusted to each other that the latter was contained 
an exact even number of times in the former ; that is, 
had it been exactly either a year or half a year; then 
we might expect a similar recurrence of the meteoric 
shower every year ; but only a slight variation in such 
a proportion between the two periods would occasion 
the repetition of the shower for a few years in succes- 
sion, and then an intermission of them, for an unknown 
length of time, until the two bodies were brought into 
the same relative situation as before. Disturbances, 
also, occasioned by the action of Venus and Mercury, 
might wholly subvert this numerical relation, and in- 
crease or diminish the probability of a repetition of the 
phenomenon. Accordingly, from the year 1830, when 
the meteoric shower of November was first observed, 
until 1833, there was a regular increase of the exhibi- 
tion ; in 1833, it came to its maximum; and after that 
time it was repeated upon a constantly diminishing 
scale, until 1838, since which time it has not been ob- 
served. Perhaps ages may roll away before the world 
will be again surprised and delighted with a display of 
celestial fire-works equal to that of the morning of No- 
vember 13, 1833. 




O, majestic Night 

Nature's great ancestor ! Day's elder bom, 

And fated to survive the transient sun ! 

By mortals and immortals seen with awe ! 

A starry crown thy raven brow adorns, 

An azure zone thy waist ; clouds, in heaven's loom 

Wrought, through varieties of shape and shade, 

In ample folds of drapery divine, 

Thy flowing mantle form} and heaven throughout 

Voluminously pour thy pompous train." Young. 

SINCE the solar system is but one among a myriad of 
worlds which astronomy unfolds, it may appear to you 
that I have dwelt too long on so diminutive a part of 
creation, and reserved too little space for the other sys- 
tems of the universe. But however humble a province 
our sun and planets compose, in the vast empire of 
Jehovah, yet it is that which most concerns us ; and it 
is by the study of the laws by which this part of crea- 
tion is governed, that we learn the secrets of the skies. 

Until recently, the observation and study of the phe- 
nomena of the solar system almost exclusively occupied 
the labors of astronomers. But Sir William Herschel 
gave his chief attention to the sidereal heavens, and 
opened new and wonderful fields of discovery, as well as 
of speculation. The same subject has been prosecuted 
with similar zeal and success by his son, Sir John Her- 
schel, and Sir James South, in England, and by Pro- 
fessor Struve, of Dorpat, until more has been actually 
achieved than preceding astronomers had ventured to 
conjecture. A limited sketch of these wonderful dis- 
coveries is all that I propose to offer you. 

The fixed stars are so called, because, to common ob- 
servation, they always maintain the same situations with 
respect to one another. The stars are classed by their 
apparent magnitudes. The whole number of magni- 
tudes recorded are sixteen, of which the first six only 
are visible to the naked eye; the rest are telescopic 


stars. These magnitudes are not determined by any 
very definite scale, but are merely ranked according to 
their relative degrees of brightness, and this is left in a 
great measure to the decision of the eye alone. The 
brightest stars, to the number of fifteen or twenty, are 
considered as stars of the first magnitude ; the fifty or 
sixty next brightest, of the second magnitude ; the next 
two hundred, of the third magnitude ; and thus the 
number of each class increases rapidly, as we descend 
the scale, so that no less than fifteen or twenty thous- 
and are included within the first seven magnitudes. 

The stars have been grouped in constellations from 
the most remote antiquity ; a few, as Orion, Bootes, and 
Ursa Major, are mentioned in the most ancient writings, 
under the same names as they bear at present. The 
names of the constellations are sometimes founded on 
a supposed resemblance to the objects to which they be- 
long ; as the Swan and the Scorpion were evidently 
so denominated from their likeness to those animals ; 
but in most cases, it is impossible for us to find any 
reason for designating a constellation by the figure of 
the animal or hero which is employed to represent it. 
These representations were probably once blended with 
the fables of pagan mythology. The same figures, ab- 
surd as they appear, are still retained for the conven- 
ience of reference ; since it is easy to find any particu- 
lar star, by specifying the part of the figure to which 
it belongs ; as when we say, a star is in the neck of 
Taurus, in the knee of Hercules, or in the tail of the 
Great Bear. This method furnishes a general clue 
to its position ; but the stars belonging to any con- 
stellation are distinguished according to their apparent 
magnitudes, as follows : First, by the Greek letters, Al- 
pha, Beta, Gamma, &c. Thus, Alpha Orionis denotes 
the largest star in Orion ; Beta Andromeda, the sec- 
ond star in Andromeda ; and Gamma Leonis, the third 
brightest star in the Lion. When the number of the 
Greek letters is insufficient to include all the stars in a 
constellation, recourse is had to the letters of the Ro- 


man alphabet, a, b, c, &c. ; and in all cases where 
these are exhausted the final resort is to numbers. 
This is evidently necessary, since the largest constella- 
tions contain many hundreds or even thousands of stars. 
Catalogues of particular stars have also been published, 
by different astronomers, each author numbering the 
individual stars embraced in his list according to the 
places they respectively occupy in the catalogue. These 
references to particular catalogues are sometimes enter- 
ed on large celestial globes. Thus we meet with a star 
marked 84 H., meaning that this is its number in Her- 
schel's catalogue ; or 140 M., denoting the place the 
star occupies in the catalogue of Mayer. 

The earliest catalogue of the stars was made by 
Hipparchus, of the Alexandrian school, about one hun- 
dred and forty years before the Christian era. A new 
star appearing in the firmament, he was induced to 
count the stars, and to record their positions, in order 
that posterity might be able to judge of the permanen- 
cy of the constellations. His catalogue contains all 
that were conspicuous to the naked eye in the latitude 
of Alexandria, being one thousand and twenty-two. 
Most persons, unacquainted with the actual number of 
the stars which compose the visible firmament, would 
suppose it to be much greater than this ; but it is found 
that the catalogue of Hipparchus embraces nearly all 
that can now be seen in the same latitude ; and that on 
the equator, where the spectator has both the northern 
and southern hemispheres in view, the number of stars 
that can be counted does not exceed three thousand. 
A careless view of the firmament in a clear night gives 
us the impression of an infinite number of stars ; but 
when we begin to count them, they appear much more 
sparsely distributed than we supposed, and large por- 
tions of the sky appear almost destitute of stars. 

By the aid of the telescope, new fields of stars pre- 
sent themselves, of boundless extent ; the number con- 
tinually augmenting, as the powers of the telescope are 
increased. Lalande, in his i Histoire Celeste/ has reg- 


istered the positions of no less than fifty thousand ; and 
the whole number visible in the largest telescopes 
amounts to many millions. 

When you look at the firmament on a clear Autum- 
nal or Winter evening, it appears so thickly studded 
with stars, that you would perhaps imagine that the 
task of learning even the brightest of them would be 
almost hopeless. Let me assure you, this is all a mis- 
take. On the contrary, it is a very easy task to be- 
come acquainted with the names and positions of the 
stars of the first magnitude, and of the leading constel- 
lations. If you will give a few evenings to the study, 
you will be surprised to find, both how rapidly you can 
form these new acquaintances, and how deeply you 
will become interested in them. I would advise you, 
at first, to obtain, for an evening or two, the assistance 
of some friend who, is familiar with the stars, just to 
point out a few of the most conspicuous constellations. 
This will put you on the track, and you will afterwards 
experience no difficulty in finding all the constellations 
and stars that are particularly worth knowing ; espec- 
ially if you have before you a map of the stars, or, what 
is much better, a celestial globe. It is a pleasant even- 
ing recreation for a small company of young astronomers 
to go out together, and learn one or two constellations 
every favorable evening, until the whole are mastered. 
If you have a celestial globe, rectify it for the evening ; 
that is, place it in such a position, that the constella- 
tions shall be seen on it in the same position with re- 
spect to the horizon, that they have at that moment in 
the sky itself. To do this, I first elevate the north 
pole until the number of degrees on the brass meridian 
from the pole to the horizon corresponds to my latitude, 
(forty-one degrees and eighteen minutes.) I then find 
the sun's place in the ecliptic, by looking for the day 
of the month on the broad horizon, and against it no- 
ting the corresponding sign and degree. I now find 
the same sign and degree on the ecliptic itself, and 
bring that point to the brass meridian. As that will 


be the position of the sun at noon, I set the hour- 
index at twelve, and then turn the globe westward, 
until the index points to the given hour of the eve- 
ning. If I now inspect the figures of the constellations, 
and then look upward at the firmament, I shall see 
that the latter are spread over the sky in the same man- 
ner as the pictures of them are painted on the globe. 
I will point out a few marks by which the leading con- 
stellations may be recognised ; this will aid you in find- 
ing them, and you can afterwards learn the individual 
stars of a constellation, to any extent you please, by means 
of the globes or maps. Let us begin with the Constel- 
lations of the Zodiac, which, succeeding each other, 
as they do, in a known order, are most easily found. 

Aries (the Rani) is a small constellation, known by 
two bright stars which form his head, Alpha and Beta 
Arietis. These two stars are about four degrees apart ; 
and directly south of Beta, at the distance of one de- 
gree, is a smaller star, Gamma Jlrietis. It has been 
already intimated that the Vernal equinox probably was 
near the head of Aries, when the signs of the zodiac 
received their present names. 

Taurus (the Bull) will be readily found by the sev- 
en stars, or Pleiades, which lie in his neck. The larg- 
est star in Taurus is Aldebaran, in the Bull's eye, a 
star of the first magnitude, of a reddish color, somewhat 
resembling the planet Mars. Aldebaran and four oth- 
er stars, close together in the face of Taurus, compose 
the Hyades. 

Gemini (the Twins) is known by two very bright 
stars, Castor and Pollux, four degrees asunder. Cas- 
tor (the northern) is of the first, and Pollux of the sec- 
ond, magnitude. 

Cancer (the Crab.) There are no large stars in this 
constellation, and it is regarded as less remarkable than 
any other in the zodiac. It contains, however, an in- 
teresting group of small stars, called Praesepe, or the 
nebula of Cancer, which resembles a comet, and is of- 
ten mistaken for one, by persons unacquainted with the 


stars. With a telescope of very moderate powers this 
nebula is converted into a beautiful assemblage of ex- 
ceedingly bright stars. 

Leo (the Lion) is a very large constellation, and has 
many interesting members. Regulus (Alpha Leonis) 
is a star of the first magnitude, which lies directly in 
the ecliptic, and is much used in astronomical obser- 
vations. North of Regulus, lies a semicircle of bright 
stars, forming a sickle, of which Regulus is the handle. 
Denebola, a star of the second magnitude, is in the Li- 
on's tail, twenty-five degrees northeast of Regulus. 

Virgo (the Virgin) extends a considerable way 
from west to east, but contains only a few bright stars. 
Spied, however, is a star of the first magnitude, and 
lies a little east of the place of the Autumnal equinox. 
Eighteen degrees eastward of Denebola, and twenty 
degrees north of Spica, is Vindemiatrix, in the arm 
of Virgo, a star of the third magnitude. 

Libra (the Balance) is distinguished by three large 
stars, of which the two brightest constitute the beam of 
the balance, and the smallest forms the top or handle. 

Scorpio (the Scorpion) is one of the finest of the 
constellations. His head is formed of five bright stars, 
arranged in the arc of a circle, which is crossed in the 
centre by the ecliptic nearly at right angles, near the 
brightest of the five, Beta Scorpionis. Nine degrees 
southeast of this is a remarkable star of the first mag- 
nitude, of a reddish color, called Cor Scorpionis, or 
Antares. South of this, a succession of bright stars 
sweep round towards the east, terminating in several 
small stars, forming the tail of the Scorpion. 

Sagittarius (the Archer.) Northeast of the tail of 
the Scorpion are three stars in the arc of a circle, which 
constitute the bow of the Archer, the central star be- 
ing the brightest, directly west of which is a bright star 
which forms the arrow. 

Capricornus (the Goat) lies northeast of Sagittarius, 
and is known by two bright stars, three degrees apart, 
which form the head, 


Aquarius (the Water-Bearer) is recognised by two 
stars in a line with Alpha Capricorni, forming the 
shoulders of the figure. These two stars are ten de- 
grees apart ; and three degrees southeast is a third star, 
which, together with the other two, make an acute tri- 
angle, of which the westernmost is the vertex. 

Pisces (the Fishes) lie between Aquarius and Aries. 
They are not distinguished by any large stars, but are 
connected by a series of small stars, that form a crook- 
ed line between them. Piscis Australia, the South- 
ern Fish, lies directly below Aquarius, and is known by a 
single bright star far in the south, having a declination 
of thirty degrees. The name of this star is Fomalhaut, 
and it is much used in astronomical measurements. 

The constellations of the zodiac, being first well 
learned, so as to be readily recognised, will facilitate 
the learning of others that lie north and south of them. 
Let us, therefore, next review the principal Northern 
Constellations, beginning north of Aries, and proceed- 
ing from west to east. 

Andromeda is characterized by three stars of the sec- 
ond magnitude, situated in a straight line, extending 
from west to east. The middle star is about seventeen 
degrees north of Beta Arietis. It is in the girdle of 
Andromeda, and is named Mirach. The other two lie 
at about equal distances, fourteen degrees west and east 
of Mirach. The western star, in the head of Androm- 
eda, lies in the equinoctial colure. The eastern star, 
Alamak, is situated in the foot. 

Perseus lies directly north of the Pleiades, and con- 
tains several bright stars. About eighteen degrees from 
the Pleiades is Algol, a star of the second magnitude, 
in the head of Medusa, which forms a part of the fig- 
ure ; and nine degrees northeast of Algol is Algenib, 
of the same magnitude, in the back of Perseus. Be- 
tween Algenib and the Pleiades are three bright stars, 
at nearly equal intervals, which compose the right leg 
of Perseus. 

Auriga (the Wagoner) lies directly east of Perseus, 


and extends nearly parallel to that constellation, from 
north to south. Capella, a very white and beautiful 
star of the first magnitude, distinguishes this constella- 
tion. The feet of Auriga are near the Bull's horns. 

The Lynx comes next, but presents nothing partic- 
ularly interesting, containing no stars above the fourth 

Leo Minor consists of a collection of small stars 
north of the sickle in Leo, and south of the Great Bear. 
Its largest star is only of the third magnitude. 

Coma Berenices is a cluster of small stars, north of 
Denebola, in the tail of the Lion, and of the head of 
Virgo. About twelve degrees directly north of Bere- 
nice's hair, is a single bright star, called Cor Caroli, or 
Charles's Heart. 

Bootes, which comes next, is easily found by means 
of Arcturus, a star of the firs-t magnitude, of a reddish 
color, which is situated near the knee of the figure. 
Arcturus is accompanied by three small stars, forming 
a triangle a little to the southwest. Two bright stars, 
Gamma and Delta Bootis, form the shoulders, and 
Beta, of the third magnitude, is in the head, of the figure. 

Corona Borealis, (the Crown,) which is situated 
east of Bootes, is very easily recognised, composed as 
it is of a semicircle of bright stars. In the centre of the 
bright crown is a star of the second magnitude, called 
Gemma : the remaining stars are all much smaller. 

Hercules, lying between the Crown on the west and 
the Lyre on the east, is very thickly set with stars, most 
of which are quite small. This constellation covers a 
great extent of the sky, especially from north to south, 
the head terminating within fifteen degrees of the equa- 
tor, and marked by a star of the third magnitude, called 
Ras Algethi, which is the largest in the constellation. 

Ophiucus is situated directly south of Hercules, ex- 
tending some distance on both sides of the equator, the 
feet resting on the Scorpion. The head terminates 
near the head of Hercules, and, like that, is marked by 
a bright star within five degrees of Alpha Herculis, 


Ophiucus is represented as holding in his hands the 
Serpent, the head of which, consisting of three bright 
stars, is situated a little south of the Crown. The folds 
of the serpent will be easily followed by a succession 
of bright stars, which extend a great way to the east. 

Aquila (the Eagle) is conspicuous for three bright 
stars in its neck, of which the central one, Altair, is a 
very brilliant white star of the first magnitude. Anti- 
nous lies directly south of the Eagle, and north of the 
head of Capricornus. 

Delphinus (the Dolphin) is a small but beautiful 
constellation, a few degrees east of the Eagle, and is 
characterized by four bright stars near to one another, 
forming a small rhombic square. Another star of the 
same magnitude, five degrees south, makes the tail. 

Pegasus lies between Aquarius on the southwest and 
Andromeda on the northeast. It contains but few large 
stars. A very regular square of bright stars is composed 
of Alpha AndromedcB and the three largest stars in 
Pegasus ; namely, Scheat, Markab, and Algenib. The 
sides composing this square are each about fifteen de- 
grees. Algenib is situated in the equinoctial colure. 

We may now review the Constellations which sur- 
round the north pole, within the circle of perpetual ap- 

Ursa Minor (the Little Bear) lies nearest the pole.. 
The pole-star, Polaris, is in the extremity of the tail, 
and is of the third magnitude. Three stars in a straight 
line, four degrees or five degrees apart, commencing 
with the pole-star, lead to a trapezium of four stars, and 
the whole seven form together a dipper, the trapezium 
being the body and the three stars the handle. 

Ursa Major (the Great Bear) is situated between 
the pole and the Lesser Lion, and is usually recognised 
by the figure of a larger and more perfect dipper which 
constitutes the hinder part of the animal. This has also 
seven stars, four in the body of the Dipper and three 
in the handle. All these are stars of much celebrity. 
The two in the western side of the Dipper, Alpha and 

32 L. A. 


Beta, are called Pointers, on account of their always 
being in a right line with the pole-star, and therefore 
affording an easy mode of finding that. The first star 
in the tail, next the body, is named Alioth, and the 
second, Mizar. The head of the Great Bear lies far to 
the westward of the Pointers, and is composed of nu- 
merous small stars ; and the feet are severally composed 
of two small stars very near to each other. 

Draco (the Dragon) winds round between the Great 
and the Little Bear ; and, commencing with the tail, 
between the Pointers and the pole-star, it is easily 
traced by a succession of bright stars extending from 
west to east. Passing under Ursa Minor, it returns 
westward, and terminates in a triangle which forms the 
head of Draco, near the feet of Hercules, northwest of 
Lyra. Cepheus lies eastward of the breast of the Drag- 
on, but has no stars above the third magnitude. 

Cassiopeia is known by the figure of a chair, com- 
posed of four stars which form the legs, and two which 
form the back. This constellation lies between Perseus 
and Cepheus, in the Milky Way. 

Cygnus (the Stvari) is situated also in the Milky 
Way, some distance southwest of Cassiopeia, towards 
the Eagle. Three bright stars, which lie along the 
Milky Way, form the body and neck of the Swan, and 
two others, in a line with the middle one of the three, 
one above and one below, constitute the wings. This 
constellation is among the few that exhibit some resem- 
blance to the animals whose names they bear. 

Lyra (the Lyre) is directly west of the Swan, and 
is easily distinguished by a beautiful white star of the 
first magnitude, Alpha Lyrce. 

The Southern Constellations are comparatively few 
in number. I shall notice only the Whale, Orion, the 
Greater and Lesser Dog, Hydra, and the Crow. 

Cetus (the Whale) is distinguished rather for its ex- 
tent than its brilliancy, reaching as it does through forty 
degrees of longitude, while none of its stars, except one, 
are above the third magnitude. Menkar (Alpha Ceti) 


in the mouth, is a star of the second magnitude ; and 
several other bright stars, directly south of Aries, make 
the head and neck of the Whale. Mira, (Omicron 
Ccti,) in the neck of the Whale, is a variable star. 

Orion is one of the largest and most beautiful of the 
constellations, lying southeast of Taurus. A cluster of 
small stars forms the head ; two large stars, Betalgeus 
of the first and Bellatrix of the second magnitude, 
make the shoulders ; three more bright stars compose 
the buckler, and three the sword ; and Rigel, another 
star of the first magnitude, makes one of the feet. In 
this constellation there are seventy stars plainly visible 
to the naked eye, including two of the first magnitude, 
four of the second, and three of the third. 

Canis Major lies southeast of Orion, and is distin- 
guished chiefly by its containing the largest of the fixed 
stars, Sirius. 

Canis Minor, a little north of the equator, between 
Canis Major and Gemini, is a small constellation, con- 
sisting chiefly of two stars, of which, Procyon is of the 
first magnitude. 

Hydra has its head near Procyon, consisting of a 
number of stars of ordinary brightness. About fifteen 
degrees southeast of the head is a star of the second 
magnitude, forming the heart, (Cor Hydra;) and 
eastward of this is a long succession of stars of the 
fourth and fifth magnitudes, composing the body and 
tail, and reaching a few degrees south of Spica Virginis. 

Corvus (the Crow) is represented as standing on 
the tail of Hydra. It consists of small stars, only three 
of which are as large as the third magnitude. 

In assigning the places of individual stars, I have not 
aimed at great precision ; but such a knowledge as you 
will acquire of the constellations and larger stars, by 
nothing more even than you can obtain from the fore- 
going sketch, will not only add greatly to the interest 
with which you will ever afterwards look at the starry 
heavens, but it will enable you to locate any phenom- 
enon that may present itself in the nocturnal sky, and 


to understand the position of any object that may be 
described, by assigning its true place among the stars ; 
although I hope you will go much further than this 
mere outline, in cultivating an actual acquaintance with 
the stars. Leaving, now, these great divisions of the 
bodies of the firmament, let us ascend to the next 
order of stars, composing CLUSTERS. 

In various parts of the nocturnal heavens are seen 
large groups which, either by the naked eye, or by the 
aid of the smallest telescope, are perceived to consist 
of a great number of small stars. Such are the Ple- 
iades, Coma Berenices, and Prsesepe, or the Bee-hive, 
in Cancer. The Pleiades, or Seven Stars, as they are 
called, in the neck of Taurus, is the most conspicuous 
cluster. When we look directly at this group, we 
cannot distinguish more than six stars ; but by turning 
the eye sideways upon it, we discover that there are 
many more ; for it is a remarkable fact that indirect 
vision is far more delicate than direct. Thus we can 
see the zodiacal light or a comet's tail much more dis- 
tinctly and better defined, if we fix one eye on a part 
of the heavens at some distance and turn the other 
eye obliquely upon the object, than we can by looking 
directly towards it. Telescopes show the Pleiades to 
contain fifty or sixty stars, crowded together, and appa- 
rently insulated from the other parts of the heavens. 
Coma, Berenices has fewer stars, but they are of a larg- 
er class than those which compose the Pleiades. The 
Bee-hive, or Nebula of Cancer, as it is called, is one 
of the finest objects of this kind for a small telescope, 
being by its aid converted into a rich congeries of shin- 
ing points. The head of Orion affords an example of 
another cluster, though less remarkable than those al- 
ready mentioned. These clusters are pleasing objects 
to the telescope ; and since a common spyglass will 
serve to give a distinct view of most of them, every 
one may have the power of taking the view. But we 
pass, now, to the third order of stars, which present 
themselves much more obscurely to the gaze of the as- 

Figures 70, 71, 72, 73. 



tronomer, and require large instruments for the full de- 
velopement of their wonderful organization. These 
are the NEBULAE. 

Nebulae are faint misty appearances which are dimly 
seen among the stars, resembling comets, or a speck of 
fog. They are usually resolved by the telescope into 
myriads of small stars; though in some instances, no 
powers of the telescope have been found sufficient thus 
to resolve them. The Galaxy or Milky Way, presents 
a continued succession of large nebulae. The telescope 
reveals to us innumerable objects of this kind. Sir 
William Herschel has given catalogues of two thousand 
nebulae, and has shown that the nebulous matter is dis- 
tributed through the immensity of space in quantities 
inconceivably great, and in separate parcels, of all 
shapes and sizes, and of all degrees of brightness be- 
tween a mere milky appearance and the condensed 
light of a fixed star. In fact, more distinct nebulae 
have been hunted out by the aid of telescopes than the 
whole number of stars visible to the naked eye in a 
clear Winter's night. Their appearances are extremely 
diversified. In many of them we can easily distinguish 
the individual stars ; in those apparently more remote, 
the interval between the stars diminishes, until it be- 
comes quite imperceptible ; and in their faintest aspect 
they dwindle to points so minute, as to be appropriate- 
ly denominated star-dust. Beyond this, no stars are 
distinctly visible, but only streaks or patches of milky 
light. The diagram facing page 379 represents a 
magnificent nebula in the Galaxy. In objects so dis- 
tant as the fixed stars, any apparent interval must de- 
note an immense space ; and just imagine, yourself sit- 
uated any where within the grand assemblage of stars, 
and a firmament would expand itself over your head 
like that of our evening sky, only a thousand times 
more rich and splendid. 

Many of the nebulae exhibit a tendency towards 
a globular form, and indicate a rapid condensation 
towards the centre. This characteristic is exhibited in 


the forms represented in Figs. 70 and 71. We have 
here two specimens of nebulae of the nearer class, 
where the stars are easily discriminated. In Figs. 72 
and 73 we have examples of two others of the remoter 
kind, one of which is of the variety called star-dust. 
These wonderful objects, however, are not confined to 
the spherical form, but exhibit great varieties of figure. 
Sometimes they appear as ovals ; sometimes they are 
shaped like a fan ; and the unresolvable kind often affect 
the most fantastic forms. The opposite diagram, Fig. 
74, as well as the preceding, affords a specimen of these 
varieties., as given in Professor Nichols's 'Architecture of 
the Heavens,' where they are faithfully copied from the 
papers of Herschel, in the ' Philosophical Transactions.' 

Sir John Herschel has recently returned from a resi- 
dence of five years at the Cape of Good Hope, with 
the express view of exploring the hidden treasures of 
the southern hemisphere. The kinds of nebulae are in 
general similar to those of the northern hemisphere, 
and the forms are equally various and singular. The 
Magellan Clouds, two remarkable objects seen among 
the stars of that hemisphere, and celebrated among 
navigators, appeared to the great telescope of Herschel 
(as we are informed by Professor Nichols) no longer 
as simple milky spots, or permanent light flocculi of 
cloud, as they appear to the unassisted eye, but shone 
with inconceivable splendor. The Nubecula Major, as 
the larger object is called, is a congeries of clusters of 
stars, of irregular form, globular clusters and nebulae 
of various magnitudes and degrees of condensation, 
among which is interspersed a large portion of irresolv- 
able nebulous matter^ which may be, and probably is, 
star-dust, but which the power of the twenty-feet tel- 
escope shows only as a general illumination of the field 
of view, forming a bright ground on which the other 
objects are scattered. The Nubecula Minor (the lesser 
cloud) exhibited appearances similar, though inferior in 

It is a grand idea, first conceived by Sir William 

Figure 74. 


Figure 75. 



Herschel, and generally adopted by astronomers, that 
the whole Galaxy, or Milky Way, is nothing else than 
a nebula, and appears so extended, merely because it 
happens to be that particular nebula to which we be- 
long. According to this view, our sun, with his atten- 
dant planets and comets, constitutes but a single star 
of the Galaxy, and our firmament of stars, or visible 
heavens, is composed of the stars of our nebula alone. 
An inhabitant of any of the other nebulae would see 
spreading over him a firmament equally spacious, and 
in some cases inconceivably more brilliant. 

It is an exalted spectacle to travel over the Galaxy 
in a clear night, with a powerful telescope, with the 
heart full of the idea that every star is a world. Sir 
William Herschel, by counting the stars in a single 
field of his telescope, estimated that fifty thousand had 
passed under his review in a zone two degrees in 
breadth, during a single hour's observation. Notwith- 
standing the apparent contiguity of the stars which 
crowd the Galaxy, it is certain that their mutual dis- 
tances must be inconceivably great. 

It is with some reluctance that I leave, for the pres- 
ent, this fairy land of astronomy ; but I must not omit, 
before bringing these Letters to a conclusion, to tell 
you something respecting other curious and interesting 
objects to be found among the stars. 

VARIABLE STARS are those which undergo a periodi- 
cal change of brightness. One of the most remarka- 
ble is the star Mira, in the Whale, (Omicron Ceti.) It 
appears once in eleven months, remains at its greatest 
brightness about a fortnight, being then, on some oc- 
casions, equal to a star of the second magnitude. It 
then decreases about three months, until it becomes 
completely invisible, and remains so about five months, 
when it again becomes visible, and continues increasing 
during the remaining three months of its period. 

Another very remarkable variable star is Algol, (Beta 
Persei.) It is usually visible as a star of the second 
magnitude, and continues such for two days and four- 


teen hours, when it suddenly begins to diminish in splen- 
dor, and in about three and a half hours is reduced to 
the fourth magnitude. It then begins again to increase, 
and in three and a half hours more is restored to its 
usual brightness, going through all its changes in less 
than three days. This remarkable law of variation 
appears strongly to suggest the revolution round it of 
some opaque body, which, when interposed between us 
and Algol, cuts off a large portion of its light. " It is," 
says Sir J. Herschel, "an indication of a high degree 
of activity in regions where, but for such evidences, we 
might conclude all lifeless. Our sun requires almost 
nine times this period to perform a revolution on its 
axis. On the other hand, the periodic time of an 
opaque revolving body, sufficiently large, which would 
produce a similar temporary obscuration of the sun, 
seen from a fixed star, would be less than fourteen 
hours." The duration of these periods is extremely 
various. While that of Beta Persei, above mentioned, 
is less than three days, others are more than a year ; 
and others, many years. 

TEMPORARY STARS are new stars, which have appear- 
ed suddenly in the firmament, and, after a certain in- 
terval, as suddenly disappeared, and returned no more. 
It was the appearance of a new star of this kind, one 
hundred and twenty-five years before the Christian era, 
that prompted Hipparchus to draw up a catalogue of 
the stars, the first on record. Such, also, was the star 
which suddenly shone out, A. D. 389, in the Eagle, as 
bright as Venus, and, after remaining three weeks, dis- 
appeared entirely. At other periods, at distant intervals, 
similar phenomena have presented themselves. Thus 
the appearance of a star in 1572 was so sudden, that 
Tycho Brahe, returning home one day, was surprised to 
find a collection of country people gazing at a star which 
he was sure did not exist half an hour before. It was 
then as bright as Sirius, and continued to increase until 
it surpassed Jupiter when brightest, and was visible at 
mid-day. In a month it began to diminish ; and, in three 


months afterwards, it had entirely disappeared. It has 
been supposed by some that, in a few instances, the 
same star has returned, constituting one of the periodical 
or variable stars of a long period. Moreover, on a 
careful reexamination of the heavens, and a compari- 
son of catalogues, many stars are now discovered to be 

DOUBLE STARS are those which appear single to the 
naked eye, but are resolved into two by the telescope ; 
or, if not visible to the naked eye, are seen in the tel- 
escope so close together as to be recognised as objects 
of this class. Sometimes, three or more stars are found 
in this near connexion, constituting triple, or multiple 
stars. Castor, for example, when seen by the naked 
eye, appears as a single star, but in a telescope even of 
moderate powers, it is resolved into two stars, of be- 
tween the third and fourth magnitudes, within five sec- 
onds of each other. These two stars are nearly of 
equal size ; but more commonly, one is exceedingly 
small in comparison with the other, resembling a satel- 
lite near its primary, although in distance, in light, and 
in other characteristics, each has all the attributes of a 
star, and the combination, therefore, cannot be that of 
a planet with a satellite. In most instances, also, the 
distance between these objects is much less than five 
seconds ; and, in many cases, it is less than one second. 
The extreme closeness, together with the exceeding mi- 
nuteness, of most of the double stars, requires the best 
telescopes united with the most acute powers of obser- 
vation. Indeed, certain of these objects are regarded 
as the severest tests both of the excellence of the instru- 
ments and of the skill of the observer. The diagram 
on page 382, Fig. 76, represents four double stars, as 
seen with appropriate magnifiers. No. 1, exhibits Ep- 
silon Bootis with a power of three hundred and fifty ; 
No. 2, Rigel, with a power of one hundred and thirty ; 
No. 3, the Pole-star, with a power of one hundred ; and 
No. 4, Castor, with a power of three hundred. 

Our knowledge of the double stars almost commenc- 


1 2 Fig. 76. 3 

ed with Sir William Herschel, about the year 1780. 
At the time he began his search for them, he was ac- 
quainted with only four. Within five years he discov- 
ered nearly seven hundred double stars, and during 
his life, he observed no less than twenty-four hundred. 
In his Memoirs, published in the Philosophical Trans- 
actions, he gave most accurate measurements of the 
distances between the two stars, and of the angle 
which a line joining the two formed with a circle paral- 
lel to the equator. These data would enable him, or 
at least posterity, to judge whether these minute bodies 
ever change their position with respect to each other. 
Since 1821, these researches have been prosecuted, 
with great zeal and industry, by Sir James South and 
Sir John Herschel, in England ; while Professor Struve, 
of Dorpat, with the celebrated telescope of Fraunho- 
fer, has published, from his own observations, a cata- 
logue of three thousand double stars, the determination 
of which involved the distinct and most minute inspec- 
tion of at least one hundred and twenty thousand stars. 
Sir John Herschel, in his recent survey of the southern 
hemisphere, is said to have added to the catalogue of 
double stars nearly three thousand more. 

Two circumstances add a high degree of interest to 
the phenomena of double stars : the first is, that a few 
of them, at least, are found to have a revolution around 
each other ; the second, that they are supposed to af- 
ford the means of ascertaining the parallax of the fixed 
stars. But I must defer these topics till my next Letter. 




" O how canst thou renounce the boundless store 
Of charms that Nature to her votary yields ? 
The warbling woodland, the resounding shore, 
The pomp of groves, and garniture of fields ; 
All that the genial ray of morning yields, 
And all that echoes to the song of even, 
All that the mountain's sheltering bosom shields, 
And all the dread magnificence of heaven, 
O how canst thou renounce, and hope to be forgiven !" Beattie. 

IN 1803, Sir William Herschel first determined and 
announced to the world, that there exist among the stars 
separate systems, composed of two stars revolving about 
each other in regular orbits. These he denominated 
binary stars, to distinguish them from other double 
stars where no such motion is detected, and whose 
proximity to each other may possibly arise from casual 
juxtaposition, or from one being in the range of the 
other. Between fifty and sixty instances of changes, 
to a greater or less amount, of the relative positions of 
double stars, are mentioned by Sir William Herschel ; 
and a few of them had changed their places so much, 
within twenty-five years, and in such order, as to lead 
him to the conclusion that they performed revolutions, 
one around the other, in regular orbits. These conclu- 
sions have been fully confirmed by later observers ; so 
that it is now considered as fully established, that there 
exist among the fixed stars binary systems, in which two 
stars perform to each other the office of sun and planet, 
and that the periods of revolution of more than one 
such pair have been ascertained with some degree of 
exactness. Immersions and emersions of stars behind 
each other have been observed, and real motions among 
them detected, rapid enough to become sensible and 
measurable in very short intervals of time. The peri- 
ods of the double stars are very various, ranging, in the 
case of those already ascertained, from forty-three years 


to one thousand. Their orbits are very small ellipses, 
only a few seconds in the longest direction, and more 
eccentric than those of the planets. A double star in 
the Northern Crown (Eta Coronet) has made a com- 
plete revolution since its first discovery, and is now far 
advanced in its second period ; while a star in the Lion 
(Gamma Leonis) requires twelve hundred years to 
complete its circuit. 

You may not at once see the reason why these revo- 
lutions of one member of a double star around the other, 
should be deemed facts of such extraordinary interest ; 
to you they may appear rather in the light of astronom- 
ical curiosities. But remark, that the revolutions of the 
binary stars have assured us of this most interesting fact, 
that the law of gravitation extends to the fixed stars. 
Before these discoveries, we could not decide, except 
by a feeble analogy, that this law transcended the 
bounds of the solar system. Indeed, our belief of the 
fact rested more upon our idea of unity of design in the 
works of the Creator, than upon any certain proof ; but 
the revolution of one star around another, in obedience 
to forces which are proved to be similar to those which 
govern the solar system, establishes the grand conclu- 
sion, that the law of gravitation is truly the law of the 
material universe. " We have the same evidence," 
says Sir John Herschel, " of the revolutions of the bi- 
nary stars about each other, that we have of those of 
Saturn and Uranus about the sun ; and the correspond- 
ence between their calculated and observed places, in 
such elongated ellipses, must be admitted to carry with 
it a proof of the prevalence of the Newtonian law of 
gravity in their systems, of the very same nature and 
cogency as that of the calculated and observed places of 
comets round the centre of our own system. But it is 
not with the revolution of bodies of a cometary or plan- 
etary nature round a solar centre, that we are now 
concerned ; it is with that of sun around sun, each, per- 
haps, accompanied with its train of planets and their 
satellites, closely shrouded from our view by the splen- 


dor of their respective suns, and crowded into a space, 
bearing hardly a greater proportion to the enormous 
interval which separates them, than the distances of 
the satellites of our planets from their primaries bear to 
their distances from the sun itself." 

Many of the double stars are of different colors ; and 
Sir John Herschel is of the opinion that there exist in 
nature suns of different colors. " It may," says he, " be 
easier suggested in words than conceived in imagina- 
tion, what variety of illumination two suns, a red and 
a green, or a yellow and a blue one, must afford to a 
planet circulating about either ; and what charming 
contrasts and ' grateful vicissitudes' a red and a green 
day, for instance, alternating with a white one and with 
darkness, might arise from the presence or absence of 
one or other or both above the horizon. Insulated stars 
of a red color, almost as deep as that of blood, occur in 
many parts of the heavens ; but no green or blue star, 
of any decided hue, has ever been noticed unassociated 
with a companion brighter than itself." 

Beside these revolutions of the binary stars, some of 
the fixed stars appear to have a real motion in space. 
There are several apparent changes of pkee among the 
stars, arising from real changes in the earth, which, as 
we are not conscious of them, we refer to the stars ; but 
there are other motions among the stars which cannot 
result from any changes in the earth, but must arise 
from changes in the stars themselves. Such motions 
are called the proper motions of the stars. Nearly two 
thousand years ago, Hipparchus and Ptolemy made the 
most accurate determinations in their power of the rel- 
ative situations of the stars, and their observations have 
been transmitted to us in Ptolemy's ( Almagest ;' from 
which it appears that the stars retain at least very near- 
ly the same places now as they did at that period. 
Still, the more accurate methods of modern astronomers 
have brought to light minute changes in the places of 
certain stars, which force upon us the conclusion, either 
that our solar system causes an apparent displacement 
33 L. A. 


of certain stars, by a motion of its own in space, of 
that they have themselves a proper motion. Possibly, 
indeed, both these causes may operate. 

If the sun, and of course the earth which accompa- 
nies him, is actually in motion, the fact may become 
manifest from the apparent approach of the stars in the 
region which he is leaving, and the recession of those 
which lie in the part of the heavens towards which he is 
travelling. Were two groves of trees situated on a 
plain at some distance apart, and we should go from one 
to the other, the trees before us would gradually appear 
further and further asunder, while those we left behind 
would appear to approach each other. Some years 
since, Sir William Herschel supposed he had detected 
changes of this kind among two sets of stars in opposite 
points of the heavens, and announced that the solar sys- 
tem was in motion towards a point in the constellation 
Hercules ; but other astronomers have not found the 
changes in question such as would correspond to this 
motion, or to any motion of the sun ; and, while it is a 
matter of general belief that the sun has a motion in 
space, the fact is not considered as yet entirely proved. 

In most cases, where a proper motion in certain stars 
has been suspected, its annual amount has been so 
small, that many years are required to assure us, that 
the effect is not owing to some other cause than a real 
progressive motion in the stars themselves ; but in a few 
instances the fact is too obvious to admit of any doubt. 
Thus, the two stars, 61 Cygni, which are nearly equal, 
have remained constantly at the same or nearly at the 
same distance of fifteen seconds, for at least fifty years 
past. Mean-while, they have shifted their local situation 
in the heavens four minutes twenty-three seconds, the 
annual proper motion of each star being five seconds 
and three tenths, by which quantity this system is every 
year carried along in some unknown path, by a motion 
which for many centuries must be regarded as uniform 
and rectilinear. A greater proportion of the double 
stars than of any other indicate proper motions, espec- 


ially the binary stars, or those which have a revolution 
around each other. Among stars not double, and no 
way differing from the rest in any other obvious partic- 
ular, a star in the constellation Cassiopeia, (Mu Cassi- 
opeia) has the greatest proper motion of any yet ascer- 
tained, amounting to nearly four seconds annually. 

You have doubtless heard much respecting the " im- 
measurable distances" of the fixed stars, and will desire 
to learn what is known to astronomers respecting this 
interesting subject. 

We cannot ascertain the actual distance of any of 
the fixed stars, but we can certainly determine that 
the nearest star is more than twenty millions of mil- 
lions of miles from the earth, (20,000,000,000,000.) 
For all measurements relating to the distances of the 
sun and planets, the radius of the earth furnishes the 
base line. The length of this line being known, and 
the horizontal parallax of the sun or any planet, we 
have the means of calculating the distance of the body 
from us, by methods explained in a previous Letter. 
But any star, viewed from the opposite sides of the 
earth, would appear from both stations to occupy pre- 
cisely the same situation in the celestial sphere, and of 
course it would exhibit no horizontal parallax. But as- 
tronomers have endeavored to find a parallax in some 
of the fixed stars, by taking the diameter of the earth's 
orbit as a base line. Yet even a change of position 
amounting to one hundred and ninety millions of miles 
proved, until very recently, insufficient to alter the 
place of a single star, so far as to be capable of detec- 
tion by very refined observations ; from which it was 
concluded that the stars have not even any annual par- 
allax ; that is, the angle subtended by the semidiameter 
of the earth's orbit, at the nearest fixed star, is insensi- 
ble. The errors to which instrumental measurements 
are subject, arising from the defects of instruments them- 
selves, from refraction, and from various other sources 
of inaccuracy, are such, that the angular determinations 
of arcs of the heavens cannot be relied on to less than 


one second, and therefore cannot be appreciated by di- 
rect measurement. It follows, that, when viewed from 
the nearest star, the diameter of the earth's orbit would 
be insensible ; the spider-line of the telescope would 
more than cover it. Taking, however, the annual par- 
allax of a fixed star at one second, it can be demon- 
strated, that the distance of the nearest fixed star must 
exceed 95000000X200000=190000000X100000, or 
one hundred thousand times one hundred and ninety 
millions of miles. Of a distance so vast we can form 
no adequate conceptions, and even seek to measure it 
only by the time that light (which moves more than one 
hundred and ninety-two thousand miles per second, and 
passes from the sun to the earth in eight minutes and 
seven seconds) would take to traverse it, which is found 
to be more than three and a half years. 

If these conclusions are drawn with respect to the 
largest of the fixed stars, which we suppose to be vastly 
nearer to us than those of the smallest magnitude, the 
idea of distance swells upon us when we attempt to es- 
timate the remoteness of the latter. As it is uncertain, 
however, whether the difference in the apparent mag- 
nitudes of the stars is owing to a real difference, or 
merely to their being at various distances from the eye, 
more or less uncertainty must attend all efforts to deter- 
mine the relative distances of the stars ; but astrono- 
mers generally believe, that the lower orders of stars are 
vastly more distant from us than the higher. Of some 
stars it is said, that thousands of years would be requir- 
ed for their light to travel down to us. 

I have said that the stars have always been held, un- 
til recently, to have no annual parallax ; yet it may be 
observed that astronomers were not exactly agreed on 
this point. Dr. Brinkley, a late eminent Irish astrono- 
mer, supposed that he had detected an annual parallax in 
Alpha Lyrae, amounting to one second and thirteen hun- 
dreths, and in Alpha Aquilae, of one second and forty- 
two hundreths. These results were controverted by Mr. 
Pond, of the Royal Observatory of Greenwich ; and 


Mr. Struve, of Dorpat, has shown that, in a number of 
cases, the supposed parallax is in a direction opposite to 
that which would arise from the motion of the earth. 
Hence it is considered doubtful whether, in all cases of 
an apparent parallax, the effect is not wholly due to er- 
rors of observation. 

But as if nothing was to be hidden from our times, 
the long sought for parallax among the fixed stars has 
at length been found, and consequently the distance of 
some of these bodies, at least, is no longer veiled in 
mystery. In the year 1838, Professor Bessel, of K6- 
ningsberg, announced the discovery of a parallax in one 
of the stars of the Swan, (61 Cygni,) amounting to 
about one third of a second. This seems, indeed, so 
small an angle, that we might have reason to suspect 
the reality of the determination ; but the most compe- 
tent judges who have thoroughly examined the process 
by which the discovery was made, assent to its validity. 
What, then, do astronomers understand, when they say 
that a parallax has been discovered in one of the fixed 
stars, amounting to one third of a second ? They mean 
that the star in question apparently shifts its place in the 
heavens, to that amount, when viewed at opposite ex- 
tremities of the earth's orbit, namely, at points in space 
distant from each other one hundred and ninety mil- 
lions of miles. On calculating the distance of the star 
from us from these data, it is found to be six hundred 
and fifty-seven thousand seven hundred times ninety- 
five millions of miles, a distance which it would take 
light more than ten years to traverse. 

Indirect methods have been proposed, for ascertain- 
ing the parallax of the fixed stars, by means of observa- 
tions on the double stars. If the two stars composing 
a double star are at different distances from us, paral- 
lax would affect them unequally, and change their rel- 
ative positions with respect to each other ; and since 
the ordinary sources of error arising from the im- 
perfection of instruments, from precession, and from 
refraction, would be avoided, (as they would affect 


both objects alike, and therefore would not disturb 
their relative positions,) measurements taken with the 
micrometer of changes much less than one second may 
be relied on. Sir John Herschel proposed a method, 
by which changes may be determined that amount to 
only one fortieth of a second. 

The immense distance of the fixed stars is inferred 
also from the fact, that the largest telescopes do not in- 
crease their apparent magnitude. They are still points, 
when viewed with glasses that magnify five thousand 

With respect to the NATURE OF THE STARS, it would 
seem fruitless to inquire into the nature of bodies so dis- 
tant, and which reveal themselves to us only as shin- 
ing points in space. Still, there are a few very satis- 
factory inferences that can be made out respecting 
them. First, the fixed stars are bodies greater than 
our earth. If this were not the case, they would not 
be visible at such an immense distance. Dr. Wollaston, 
a distinguished English philosopher, attempted to esti- 
mate the magnitudes of certain of the fixed stars from 
the light which they afford. By means of an accurate 
photometer, (an instrument for measuring the relative 
intensities of light,) he compared the light of Sirius 
with that of the sun. He next inquired how far the 
sun must be removed from us, in order to appear no 
brighter than Sirius. He found the distance to be one 
hundred and forty-one thousand times its present dis- 
tance. But Sirius is more than two hundred thousand 
times as far off as the sun ; hence he inferred that, 
upon the lowest computation, it must actually give 
out twice as much light as the sun ; or that, in point 
of splendor, Sirius must be at least equal to two suns. 
Indeed, he has rendered it probable, that its light is 
equal to that of fourteen suns. There is reason, how- 
ever, to believe that the stars are actually of various 
magnitudes, and that their apparent difference is not 
owing merely to their different distances. Bessel es- 
timates the quantity of matter in the two members of a 


double star in the Swan, as less than half that of the 

Secondly, the fixed stars are suns. We have al- 
ready seen that they are large bodies ; that they are 
immensely further off than the furthest planet ; that 
they shine by their own light ; in short, that their ap- 
pearance is, in all respects, the same as the sun would 
exhibit if removed to the region of the stars. Hence 
we infer that they are bodies of the same kind with 
the sun. We are justified, therefore, by a sound anal- 
ogy, in concluding that the stars were made for the 
same end as the sun, namely, as the centres of attrac- 
tion to other planetary worlds, to which they severally 
dispense light and heat. Although the starry heavens 
present, in a clear night, a spectacle of unrivalled gran- 
deur and beauty, yet it must be admitted that the chief 
purpose of the stars could not have been to adorn the 
night, since by far the greater part of them are invisible 
to the naked eye ; nor as landmarks to the navigator, 
for only a very small proportion of them are adapted 
to this purpose ; nor, finally, to influence the earth by 
their attractions, since their distance renders such an 
effect entirely insensible. If they are suns, and if they 
exert no important agencies upon our world, but are 
bodies evidently adapted to the same purpose as our 
sun, then it is as rational to suppose that they were 
made to give light and heat, as that the eye was made 
for seeing and the ear for hearing. It is obvious to in- 
quire, next, to what they dispense these gifts, if not to 
planetary worlds ; and why to planetary worlds, if not 
for the use of percipient beings ? We are thus led, al- 
most inevitably, to the idea of a plurality of worlds ; 
and the conclusion is forced upon us, that the spot 
which the Creator has assigned to us is but a humble 
province in his boundless empire. 




" O how unlike the complex works of man, 
Heaven's easy, artless, unincumbered, plan." Coivper. 

HAVING now explained to you, as far as I am able 
to do it in so short a space, the leading phenomena of 
the heavenly bodies, it only remains to inform you of 
the different systems of the world which have prevail- 
ed in different ages, a subject which will necessarily 
involve a sketch of the history of astronomy. 

By a system of the world, I understand an explana- 
tion of the arrangement of all the bodies that compose 
the material universe, and of their relations to each oth- 
er. It is otherwise called the ' Mechanism of the Heav- 
ens ;' and indeed, in the system of the world, we figure 
to ourselves a machine, all parts of which have a mutual 
dependence, and conspire to one great end. "The 
machines that were first invented," says Adam Smith, 
" to perform any particular movement, are always the 
most complex ; and succeeding artists generally discover 
that, with fewer wheels, and with fewer principles of 
motion, than had originally been employed, the same 
effects may be more easily produced. The first sys- 
tems, in the same manner, are always the most complex ; 
and a particular connecting chain or principle is gener- 
rally thought necessary, to unite every two seemingly 
disjointed appearances ; but it often happens, that one 
great connecting principle is afterwards found to be 
sufficient to bind together all the discordant phenomena 
that occur in a whole species of things !" This remark 
is strikingly applicable to the origin and progress of sys- 
tems of astronomy. It is a remarkable fact in the his- 
tory of the human mind, that astronomy is the oldest 
of the sciences, having been cultivated, with no small 
success, long before any attention was paid to the causes 


of the common terrestrial phenomena. The opinion 
has always prevailed among those who were unenlight- 
ened by science, that very extraordinary appearances 
in the sky, as comets, fiery meteors, and eclipses, are 
omens of the wrath of heaven. They have, therefore, 
in all ages, been watched with the greatest attention : 
and their appearances have been minutely recorded by 
the historians of the times. The idea, moreover, that 
the aspects of the stars are connected with the destinies 
of individuals and of empires, has been remarkably 
prevalent from the earliest records of history down to a 
very late period, and, indeed, still lingers among the 
uneducated and credulous. This notion gave rise to 
ASTROLOGY, an art which professed to be able, by a 
knowledge of the varying aspects of the planets and 
stars, to penetrate the veil of futurity, and to foretel ap- 
proaching irregularities of Nature herself, and the for- 
tunes of kingdoms and of individuals. That department 
of astrology which took cognizance of extraordinary 
occurrences in the natural world, as tempests, earth- 
quakes, eclipses, and volcanoes, both to predict their 
approach and to interpret their meaning, was called 
natural astrology : that which related to the fortunes 
of men and of empires, judicial astrology. Among 
many ancient nations, astrologers were held in the high- 
est estimation, and were kept near the persons of mon- 
archs ; and the practice of the art constituted a lucra- 
tive profession throughout the middle ages. Nor were 
the ignorant and uneducated portions of society alone 
the dupes of its pretensions. Hippocrates, the c Father 
of Medicine,' ranks astrology among the most important 
branches of knowledge to the physician ; and Tycho 
Brahe, and Lord Bacon, were firm believers in its mys- 
teries. Astrology, fallacious as it was, must be acknowl- 
edged to have rendered the greatest services to astron- 
omy, by leading to the accurate observation and diligent 
study of the stars. 

At a period of very remote antiquity, astronomy was 
cultivated in China, India, Chaldea, and Egypt. The 


Chaldeans were particularly distinguished for the accu- 
racy and extent of their astronomical observations. Ca- 
listhenes, the Greek philosopher who accompanied Al- 
exander the Great in his Eastern conquests, transmitted 
to Aristotle a series of observations made at Babylon 
nineteen centuries before the capture of that city by 
Alexander ; and the wise men of Babylon and the Chal- 
dean astrologers are referred to in the Sacred Writings. 
They enjoyed a clear sky and a mild climate, and their 
pursuits as shepherds favored long-continued observa- 
tions ; while the admiration and respect accorded to 
the profession, rendered it an object of still higher am- 

In the seventh century before the Christian era, as- 
tronomy began to be cultivated in Greece ; and there 
arose successively three celebrated astronomical schools, 
the school of Miletus, the school of Crotona, and the 
school of Alexandria. The first was established by 
Thales, six hundred and forty years before Christ ; the 
second, by Pythagoras, one hundred and forty years 
afterwards ; and the third, by the Ptolemies of Egypt, 
about three hundred years before the Christian era 
As Egypt and Babylon were renowned among the most 
ancient nations, for their knowledge of the sciences, 
long before they were cultivated in Greece, it was the 
practice of the Greeks, when they aspired to the char- 
acter of philosophers and sages, to resort to these coun- 
tries to imbibe wisdom at its fountains. Thales, after 
extensive travels in Crete and Egypt, returned to his 
native place, Miletus, a town on the coast of Asia Minor, 
where he established the first school of astronomy in 
Greece. Although the minds of these ancient astron- 
omers were beclouded with much error, yet Thales 
taught a few truths which do honor to his sagacity. 
He held that the stars are formed of fire ; that the 
moon receives her light from the sun, and is invisible 
at her conjunctions because she is hid in the sun's rays. 
He taught the sphericity of the earth, but adopted the 
common error of placing it in the centre of the world. 


He introduced the division of the sphere into five 
zones, and taught the obliquity of the ecliptic. He 
was acquainted with the Saros, or sacred period of the 
Chaldeans, (see page 192,) and employed it in calcu- 
lating eclipses. It was Thales that predicted the fa- 
mous eclipse of the sun which terminated the war be- 
tween the Lydians and the Medes, as mentioned in a 
former Letter. Indeed, Thales is universally regarded 
as a bright but solitary star, glimmering through mists 
on the distant horizon. 

To Thales succeeded, in the school of Miletus, two 
other astronomers of much celebrity, Anaximander and 
Anaxagoras. Among many absurd things held by Anax- 
imander, he first taught the sublime doctrine that the 
planets are inhabited, and that the stars are suns of 
other systems. Anaxagoras attempted to explain all 
the secrets of the skies by natural causes. His reason- 
ings, indeed, were alloyed with many absurd notions ; 
but still he alone, among the astronomers, maintained 
the existence of one God. His doctrines alarmed his 
countrymen, by their audacity and impiety to their 
gods, whose prerogatives he was thought to invade ; 
and, to deprecate their wrath, sentence of death was 
pronounced on the philosopher and all his family, a 
sentence which was commuted only for the sad alter- 
native of perpetual banishment. The very genius of 
the heathen mythology was at war with the truth. 
False in itself, it trained the mind to the love of what 
was false in the interpretation of nature ; it arrayed 
itself against the simplicity of truth, and persecuted and 
put to death its most ardent votaries. The religion of 
the Bible, on the other hand, lends all its aid to truth 
in nature as well as in morals and religion. In its very 
genius it inculcates and inspires the love of truth ; it 
suggests, by its analogies, the existence of established 
laws in the system of the world ; and holds out the 
moon and the stars, which the Creator has ordained, 
as fit objects to give us exalted views of his glory and 


Pythagoras was the founder of the celebrated school 
of Crotona. He was a native of Samos, an island in 
the JEgean sea, and flourished about five hundred years 
before the Christian era. After travelling more than 
thirty years in Egypt and Chaldea, and spending sev- 
eral years more at Sparta, to learn the laws and institu- 
tions of Lycurgus, he returned to his native island to 
dispense the riches he had acquired to his countrymen. 
But they, probably fearful of incurring the displeasure 
of the gods by the freedom with which he inquired into 
the secrets of the skies, gave him so unwelcome a 
reception, that he retired from them, in disgust, and 
established his school at Crotona, on the southeastern 
coast of Italy. Hither, as to an oracle, the fame of his 
wisdom attracted hundreds of admiring pupils, whom 
he instructed in every species of knowledge. From 
the visionary notions which are generally understood to 
have been entertained on the subject of astronomy, by 
the ancients, we are apt to imagine that they knew less 
than they actually did of the truths of this science. 
But Pythagoras was acquainted with many important 
facts in astronomy, and entertained many opinions re- 
specting the system of the world, which are now held 
to be true. Among other things well known to Py- 
thagoras, either derived from his own investigations, or 
received from his predecessors, were the following ; and 
we may note them as a synopsis of the state of astro- 
nomical knowledge at that age of the world. First, 
the principal constellations. These had begun to be 
formed in the earliest ages of the world. Several of 
them, bearing the same name as at present, are men- 
tioned in the writings of Hesiod and Homer ; and the 
" sweet influences of the Pleiades," and the " bands of 
Orion," are beautifully alluded to in the book of Job. 
Secondly, eclipses. Pythagoras knew both the causes 
of eclipses and how to predict them ; not, indeed, in 
the accurate manner now practised, but by means of 
the Saros. Thirdly, Pythagoras had divined the true 
system of the world, holding that the sun, and not the 


earth, (as was generally held by the ancients, even for 
many ages after Pythagoras,) is the centre around 
which all the planets revolve ; and that the stars are so 
many suns, each the centre of a system like our own. 
Among lesser things, he knew that the earth is round ; 
that its surface is naturally divided into five zones ; and 
that the ecliptic is inclined to the equator. He also 
held that the earth revolves daily on its axis, and year- 
ly around the sun ; that the galaxy is an assemblage of 
small stars ; and that it is the same luminary, namely, 
Venus, that constitutes both the morning and evening 
star ; whereas all the ancients before him had suppos- 
ed that each was a separate planet, and accordingly 
the morning star was called Lucifer, and the evening 
star, Hesperus. He held, also, that the planets were 
inhabited, and even went so far as to calculate the 
size of some of the animals in the moon. Pythagoras 
was also so great an enthusiast in music, that he not 
only assigned to it a conspicuous place in his system of 
education, but even supposed that the heavenly bodies 
themselves were arranged at distances corresponding 
to the intervals of the diatonic scale, and imagined them 
to pursue their sublime march to notes created by their 
own harmonious movements, called the ' music of the 
spheres ;' but he maintained that this celestial concert,, 
though loud and grand, is not audible to the feeble or- 
gans of man, but only to the gods. With few exceptions^ 
however, the opinions of Pythagoras on the system of the 
world were founded in truth. Yet they were reject- 
ed by Aristotle, and by most succeeding astronomers, 
down to the time of Copernicus ; and in their place 
was substituted the doctrine of crystalline spheres, first 
taught by Eudoxus, who lived about three hundred and 
seventy years before Christ. According to this system, 
the heavenly bodies are set like gems in hollow solid 
orbs, composed of crystal so transparent, that no ante- 
rior orb obstructs in the least the view of any of the 
orbs that lie behind it. The sun and the planets have 
each its separate orb ; but the fixed stars are all set in 
34 L. A. 


the same grand orb ; and beyond this is another still, 
the primum mobile, which revolves daily, from east 
to west, and carries along with it all the other orbs. 
Above the whole spreads the grand empyrean, or third 
heavens, the abode of perpetual serenity. 

To account for the planetary motions, it was sup- 
posed that each of the planetary orbs, as well as that 
of the sun, has a motion of its own, eastward, while it 
partakes of the common diurnal motion of the starry 
sphere. Aristotle taught that these motions are effected 
by a tutelary genius of each planet, residing in it, and 
directing its motions, as the mind of man directs his 

Two hundred years after Pythagoras, arose the fa- 
mous school of Alexandria, under the Ptolemies. These 
\vere a succession of Egyptian kings, and are not to 
be confounded with Ptolemy, the astronomer. By the 
munificent patronage of this enlightened family, for the 
space of three hundred years, beginning at the death 
of Alexander the Great, from whom the eldest of the 
Ptolemies had received his kingdom, the school of Al- 
exandria concentrated in its vast library and princely 
halls, erected for the accommodation of the philoso- 
phers, nearly all the science and learning of the world. 
In wandering over the immense territories of ignorance 
and barbarism which covered, at that time, almost the 
entire face of the earth, the eye reposes upon this little 
spot, as upon a verdant island in the midst of the des- 
ert. Among the choice fruits that grew in this garden 
of astronomy were several of the most distinguished 
ornaments of ancient science, of whom the most emi- 
nent were Hipparchus and Ptolemy. Hipparchus is 
justly considered as the Newton of antiquity. He 
sought his knowledge of the heavenly bodies not in the 
illusory suggestions of a fervid imagination, but in the 
vigorous application of an intellect of the first order. 
Previous to this period, celestial observations were 
made chiefly with the naked eye : but Hipparchus was 
in possession of instruments for measuring angles, and 


knew how to resolve spherical triangles. These were 
great steps beyond all his predecessors. He ascer- 
tained the length of the year within six minutes of the 
truth. He discovered the eccentricity, or elliptical fig- 
ure, of the solar orbit, although he supposed the sun 
actually to move uniformly in a circle, but the earth to 
be placed out of the centre. He also determined the 
positions of the points among the stars where the earth 
is nearest to the sun, and where it is most remote 
from it. He formed very accurate estimates of the ob- 
liquity of the ecliptic and of the precession of the equi- 
noxes. He computed the exact period of the synodic 
revolution of the moon, and the inclination of the lu- 
nar orbit ; discovered the backward motion of her node 
and of her line of apsides ; and made the first attempts 
to ascertain the horizontal parallaxes of the sun and 
moon. Upon the appearance of a new star in the fir- 
mament, he undertook, as already mentioned, to num- 
ber the stars, and to assign to each its true place in the 
heavens, in order that posterity might have the means 
of judging what changes, if any, were going forward 
among these apparently unalterable bodies. 

Although Hipparchus is generally considered as be- 
longing to the Alexandrian school, yet he lived at 
Rhodes, and there made his astronomical observations, 
about one hundred and forty years before the Christian 
era. None of his writings have come down to us ; but 
his principal discoveries have been transmitted through 
the ' Almagest' of Ptolemy. Ptolemy flourished at Al- 
exandria nearly three centuries after Hipparchus, in 
the second century after Christ. His great work, the 
' Almagest,' which has conveyed to us most that we 
know respecting the astronomical knowledge of the 
ancients, was the universal text-book of astronomers 
for fourteen centuries. 

The name of this celebrated astronomer has also 
descended to us, associated with the system of the 
world which prevailed from Ptolemy to Copernicus, 
called the Ptolemaic System. The doctrines of the 


Ptolemaic system did not originate with Ptolemy, but, 
being digested by him out of materials furnished by 
various hands, it has come down to us under the sanc- 
tion of his name. According to this system, the earth 
is the centre of the universe, and all the heavenly 
bodies daily revolve around it, from east to west. But 
although this hypothesis would account for the appar- 
ent diurnal motion of the firmament, yet it would not 
account for the apparent annual motion of the sun, nor 
for the slow motions of the planets from west to east. 
In order to explain these phenomena, recourse was had 
to deferents and epicycles, an explanation devised by 
Apollonius, one of the greatest geometers of antiquity. 
He conceived that, in the circumference of a circle, 
having the earth for its centre, there moves the centre 
of a smaller circle in the circumference of which the 
planet revolves. The circle surrounding the earth 
was called the deferent, while the smaller circle, whose 
centre was always in the circumference of the deferent, 
was called the epicycle. Thus, if E, Fig. 77, represents 

the earth, ABC will be the 
deferent, and D F G, the epicy- 
cle ; and it is obvious that the 
motion of a body from west 
to east, in this small circle, 
would be alternately direct, 
stationary, and retrograde, as 
was explained, in a previous 
Letter, to be actually the case 
with the apparent motions of 
the planets. The hypothesis, 
however, is inconsistent with 
the phases of Mercury and 
Venus, which, being between us and the sun, on 
both sides of the epicycle, would present their dark 
sides towards us at both conjunctions with the sun, 
whereas, at one of the conjunctions, it is known 
that they exhibit their disks illuminated. It is, more- 
over, absurd to speak of a geometrical centre, which 


has no bodily existence, moving round the earth on the 
circumference of another circle. In addition to these 
absurdities, the whole Ptolemaic system is encumbered 
with the following difficulties : First, it is a mere hy- 
pothesis, having no evidence in its favor except that it 
explains the phenomena. This evidence is insufficient 
of itself, since it frequently happens that each of two 
hypotheses, which are directly opposite to each other, 
will explain all the known phenomena. But the Ptole- 
maic system does not even do this, as it is inconsistent 
with the phases of Mercury and Venus, as already ob- 
served. Secondly, now that we are acquainted with 
the distances of the remoter planets, and especially the 
fixed stars, the swiftness of motion, implied in a daily 
revolution of the starry firmament around the earth, 
renders such a motion wholly incredible. Thirdly, the 
centrifugal force which would be generated in these 
bodies, especially in the sun, renders it impossible that 
they can continue to revolve around the earth as a cen- 
tre. Absurd, however, as the system of Ptolemy was, 
for many centuries no great philosophic genius appeared 
to expose its fallacies, and it therefore guided the faith 
of astronomers of all countries down to the time of 

After the age of Ptolemy, the science made little 
progress. With the decline of Grecian liberty, the 
arts and sciences declined also ; and the Romans, then 
masters of the world, were ever more ambitious to gain 
conquests over man than over matter ; and they accord- 
ingly never produced a single great astronomer. Dur- 
ing the middle ages, the Arabians were almost the only 
astronomers, and they cultivated this noble study chiefly 
as subsidiary to astrology. 

At length, in the fifteenth century, Copernicus arose, 
and after forty years of intense study and meditation, 
divined the true system of the world. You will recol- 
lect that the Copernican system maintains, 1. That the 
apparent diurnal motions of the heavenly bodies, from 
east to west, is owing to the -real revolution of the earth 


on its own axis from west to east ; and, 2. That the 
sun is the centre around which the earth and planets 
all revolve from west to east. It rests on the following 
arguments : In the first place, the earth revolves on its 
own axis. First, because this supposition is vastly more 
simple. Secondly, it is agreeable to analogy, since 
all the other planets that afford any means of determin- 
ing the question, are seen to revolve on their axes. 
Thirdly, the spheroidal figure of the earth is the fig- 
ure of equilibrium, that results from a revolution on its 
axis. Fourthly, the diminished weight of bodies at 
the equator indicates a centrifugal force arising from 
such a revolution. Fifthly, bodies let fall from a high 
eminence, fall eastward of their base, indicating that 
when further from the centre of the earth they were 
subject to a greater velocity, which, in consequence of 
their inertia, they do not entirely lose in descending to 
the lower level. 

In the second place, the planets, including the earth, 
revolve about the sun. First, the phases of Mercury 
and Venus are precisely such, as would result from 
their circulating around the sun in orbits within that 
of the earth ; but they are never seen in opposition, 
as they would be, if they circulate around the earth. 
Secondly, the superior planets do indeed revolve around 
the earth ; but they also revolve around the sun, as is 
evident from their phases, and from the known dimen- 
sions of their orbits ; and that the sun, and not the 
earth, is the centre of their motions, is inferred from 
the greater symmetry of their motions, as referred to 
the sun, than as referred to the earth ; and especially 
from the laws of gravitation, which forbid our suppos- 
ing that bodies so much larger than the earth, as some 
of these bodies are, can circulate permanently around 
the earth, the latter remaining all the while at rest. 

In the third place, the annual motion of the earth it- 
self is indicated also by the most conclusive arguments. 
For, first, since all the planets, with their satellites and 
the comets, revolve about the sun, analogy leads us to 


infer the same respecting the earth and its satellite, as 
those of Jupiter and Saturn, and indicates that it is a law 
of the solar system that the smaller bodies revolve about 
the larger. Secondly, on the supposition that the earth 
performs an annual revolution around the sun, it is em- 
braced along with the planets, in Kepler's law, that the 
squares of the times are as the cubes of the distances ; 
otherwise, it forms an exception, and the only known 
exception, to this law. 

Such are the leading arguments upon which rests the 
Copernican system of astronomy. They were, howev- 
er, only very partially known to Copernicus himself, as 
the state both of mechanical science, and of astronom 
ical observation, was not then sufficiently matured to 
show him the strength of his own doctrine, since he 
knew nothing of the telescope, and nothing of the prin- 
ciple of universal gravitation. The evidence of this 
beautiful system being left by Copernicus in so imperfect 
a state, and indeed his own reasonings in support of it 
being tinctured with some errors, we need not so much 
wonder that Tycho Brahe, who immediately followed 
Copernicus, did not give it his assent, but, influenced 
by certain passages of Scripture, he still maintained, 
with Ptolemy, that the earth is in the centre of the uni- 
verse ; and he accounted for the diurnal motions in the 
same manner as Ptolemy had done, namely, by an ac- 
tual revolution of the whole host of heaven around the 
earth every twenty-four hours. But he rejected the 
scheme of deferents and epicycles, and held that the 
moon revolves about the earth as the centre of her mo- 
tions ; but that the sun and not the earth is the centre 
of the planetary motions ; and that the sun, accompa- 
nied by the planets, moves around the earth once a 
year, somewhat in the manner in which we now con- 
ceive of Jupiter and his satellites as revolving around 
the sun. This system is liable to most of the objections 
that lie against the Ptolemaic system, with the disad- 
vantage of being more complex. 

Kepler and Galileo, however, as appeared in the 


sketch of their lives, embraced the theory of Copernicus 
with great avidity, and all their labors contributed to 
swell the evidence of its truth. When we see with 
what immense labor and difficulty the disciples of Ptol- 
emy sought to reconcile every new phenomenon of the 
heavens with their system, and then see how easily and 
naturally all the successive discoveries of Galileo and 
Kepler fall in with the theory of Copernicus, we feel 
the full force of those beautiful lines of Cowper which 
I have chosen for the motto of this Letter. 

Newton received the torch of truth from Galileo, and 
transmitted it to his successors, with its light enlarged 
and purified ; and since that period, every new discov- 
ery, whether the fruit of refined instrumental observa- 
tion or of profound mathematical analysis, has only 
added lustre to the glory of Copernicus. 

With Newton commenced a new and wonderful era 
in astronomy, distinguished above all others, not merely 
for the production of the greatest of men, but also for 
the establishment of those most important auxiliaries to 
our science, the Royal Society of London, the Academy 
of Sciences at Paris, and the Observatory of Greenwich. 
I may add the commencement of the Transactions of 
the Royal Society, and the Memoirs of the Academy of 
Sciences, which have been continued to the present 
time, both precious storehouses of astronomical riches. 
The Observatory of Greenwich, moreover, has been un- 
der the direction of an extraordinary succession of great 
astronomers. Their names are Flamstead, Halley, Brad- 
ley, Maskeleyne, Pond, and Airy, the last being still 
at his post, and worthy of continuing a line so truly il- 
lustrious. The observations accumulated at this cele- 
brated Observatory are so numerous, and so much supe- 
rior to those of any other institution in the world, that 
it has been said that astronomy would suffer little, if all 
other contemporary observations of the same kind were 
annihilated. Sir William Herschel, however, labored 
chiefly in a different sphere. The Astronomers Royal 
devoted themselves not so much to the discovery of 


new objects among the heavenly bodies, as to the exact 
determination of the places of the bodies already known, 
and to the developement of new laws or facts among 
the celestial motions. But Herschel, having construct- 
ed telescopes of far greater reach than any ever used 
before, employed them to sound new and untried depths 
in the profundities of space. We have already seen 
what interesting and amazing discoveries he made of 
double stars, clusters, and nebulae. 

The English have done most for astronomy in obser- 
vation and discovery ; but the French and Germans, in 
developing, by the most profound mathematical investi- 
gation, the great laws of physical astronomy. 

It only remains to inquire, whether the Copernican 
system is now to be regarded as a full exposition of the 
' Mechanism of the Heavens/ or whether there subsist 
higher orders of relations between the fixed stars them- 

The revolutions of the binary stars afford conclusive 
evidence of at least subordinate systems of suns, gov- 
erned by the same laws as those which regulate the 
motions of the solar system. The nebulce also compose 
peculiar systems, in which the members are evidently 
bound together by some common relation. 

In these marks of organization, of stars associated 
together in clusters ; of sun revolving around sun ; and 
of nebulae disposed in regular figures, we recognise 
different members of some grand system, links in one 
great chain that binds together all parts of the universe ; 
as we see Jupiter and his satellites combined in one 
subordinate system, and Saturn and his satellites in an- 
other, each a vast kingdom, and both uniting with a 
number of other individual parts, to compose an empire 
still more vast. 

This fact being now established, that the stars are 
immense bodies, like the sun, and that they are subject 
to the laws of gravitation, we cannot conceive how they 
can be preserved from falling into final disorder and 
ruin, unless they move in harmonious concert, like the 


members of the solar system. Otherwise, those that 
are situated on the confines of creation, being retained 
by no forces from without, while they are subject to the 
attraction of all the bodies within, must leave their sta- 
tions, and move inward with accelerated velocity ; and 
thus all the bodies in the universe would at length fall 
together in the common centre of gravity. The im- 
mense distance at which the stars are placed from each 
other would indeed delay such a catastrophe ; but this 
must be the ultimate tendency of the material world, 
unless sustained in one harmonious system by nicely- 
adjusted motions. To leave entirely out of view our 
confidence in the wisdom and preserving goodness of 
the Creator, and reasoning merely from what we know 
of the stability of the solar system, we should be justi- 
fied in inferring, that other worlds are not subject to 
forces which operate only to hasten their decay, and to 
involve them in final ruin. 

We conclude, therefore, that the material universe 
is one great system ; that the combination of planets 
with their satellites constitutes the first or lowest order 
of worlds ; that next to these, planets are linked to 
suns ; that these are bound to other suns, composing 
a still higher order in the scale of being ; and finally, 
that all the different systems of worlds move around 
their common centre of gravity. 



Philosophy, baptized 

-- , 

In the pure fountain of Eternal Love, 
Has eyes indeed ; and, viewing all she sees 
As meant to indicate a God to man, 
Gives Him the praise, and forfeits not her own." Cowper. 

I INTENDED, my dear Friend, to comply with your 
request " that I would discuss the arguments which as- 


tronomy affords to natural theology ;" but these Letters 
have been already extended so much further than I an- 
ticipated, that I shall conclude with suggesting a few 
of those moral and religious reflections, which ought al- 
ways to follow in the train of such a survey of the heav- 
enly bodies as we have now taken. 

Although there is evidence enough in the structure, 
arrangement, and laws, which prevail among the heav- 
enly bodies, to prove the existence of God, yet I think 
there are many subordinate parts of His works far bet- 
ter adapted to this purpose than these, being more fully 
within our comprehension. It was intended, no doubt, 
that the evidence of His being should be accessible to 
all His creatures, and should not depend on a kind of 
knowledge possessed by comparatively few. The mech- 
anism of the eye is probably not more perfect than 
that of the universe ; but we can analyze it better, and 
more fully understand the design of each part. But the 
existence of God being once proved, and it being 
admitted that He is the Creator and Governor of the 
world, then the discoveries of astronomy are admirably 
adapted to perform just that office in relation to the 
Great First Cause, which is assigned to them in the Bi- 
ble, namely, " to declare the glory of God, and to show 
His handiwork." In other words, the discoveries of 
astronomy are peculiarly fitted, more so, perhaps, than 
any other department of creation, to exhibit the uni- 
ty, power, and wisdom, of the Creator. 

The most modern discoveries have multiplied the 
proofs of the unity of God. It has usually been offer- 
ed as sufficient evidence of the truth of this doctrine, 
that the laws of Nature are found to be uniform when 
applied to the utmost bounds of the solar system ; that 
the law of gravitation controls alike the motions of Mer- 
cury, and those of Uranus ; and that its operation is one 
and the same upon the moon and upon the satellites 
of Saturn. It was, however, impossible, until recently, 
to predicate the same uniformity in the great laws of 
the universe respecting the. starry worlds, except by a 


feeble analogy. However improbable, it was still possi- 
ble, that in these distant worlds other laws might pre- 
vail, and other Lords exercise dominion. But the dis- 
covery of the revolutions of the binary stars, in exact 
accordance with the law of gravitation, not merely in 
a single instance, but in many instances, in all cases, 
indeed, wherever those revolutions have advanced so 
far as to determine their law of action, gives us demon- 
stration, instead of analogy, of the prevalence of the 
same law among the other systems as that which rules 
in ours. 

The marks of a still higher organization in the struc- 
ture of clusters and nebulae, all bearing that same char- 
acteristic union of resemblance and variety which be- 
longs to all the other works of creation that fall under 
our notice, speak loudly of one, and only one, grand de- 
sign. Every new discovery of the telescope, therefore, 
has added new proofs to the great truth that God is 
one : nor, so far as I know, has a single fact appeared, 
that is not entirely consonant with it. Light, more- 
over, which brings us intelligence, and, in most cases, 
the only intelligence we have, of these remote orbs, tes- 
tifies to the same truth, being similar in its properties 
and uniform in its motions, from whatever star it em- 

In displays of the power of Jehovah, nothing can 
compare with the starry heavens. The magnitudes, 
distances, and velocities, of the heavenly bodies are so 
much beyond every thing of this kind which belongs 
to things around us, from which we borrowed our first 
ideas of these qualities, that we can scarcely avoid look- 
ing with incredulity at the numerical results to which 
the unerring principles of mathematics have conducted 
us. And when we attempt to apply our measures to 
the fixed stars, and especially to the nebulae, the result 
is absolutely overwhelming : the mind refuses its aid in 
our attempts to grasp the great ideas. Nor less conspic- 
uous, among the phenomena of the heavenly bodies, is 
the wisdom of the Creator. In the first place, this at- 


tribute is every where exhibited in the happy adap- 
tation of means to their ends. No principle can be 
imagined more simple, and at the same time more ef- 
fectual to answer the purposes which it serves, than 
gravitation. No position can be given to the sun and 
planets so fitted, as far as we can judge, to fulfil their 
mutual relations, as that which the Creator has given 
them. I say, as far as we can judge ; for we find this 
to be the case in respect to our own planet and its at- 
tendant satellite, and hence have reason to infer that 
the same is the case in the other planets, evidently 
holding, as they do, a similar relation to the sun. Thus 
the position of the earth at just such a distance from 
the sun as suits the nature of its animal and vegetable 
kingdoms, and confining the range of solar heat, vast 
as it might easily become, within such narrow bounds ; 
the inclination of the earth's axis to the plane of its 
orbit, so as to produce the agreeable vicissitudes of the 
seasons, and increase the varieties of animal and veg- 
etable life, still confining the degree of inclination so 
exactly within the bounds of safety, that, were it much 
to transcend its present limits, the changes of tempera- 
ture of the different seasons would be too sudden and 
violent for the existence of either animals or vegetables ; 
the revolution of the earth on its axis, so happily di- 
viding time into hours of business and of repose ; the 
adaptation of the moon to the earth, so as to afford to 
us her greatest amount of light just at the times when- 
it is needed most, and giving to the moon just such a 
quantity of matter, and placing her at just such a dis- 
tance from the earth, as serves to raise a tide produc- 
tive of every conceivable advantage, without the evils 
which would result from a stagnation of the waters on 
the one hand, or from their overflow on the other ; 
these are a few examples of the wisdom displayed in 
the mutual relations instituted between the sun, the 
earth, and the moon. 

In the second place, similar marks of wisdom are ex- 
hibited in the many useful and important purposes 
35 L. A. 


which the same thing is mode to serve. Thus the sun 
is at once the great regulator of the planetary motions, 
and the fountain of light and heat. The moon both 
gives light by night and raises the tides. Or, if we 
would follow out this principle where its operations are 
more within our comprehension, we may instance the 
atmosphere. When man constructs an instrument, he 
deems it sufficient if it fulfils one single purpose ; as the 
watch, to tell the hour of the day, or the telescope, to 
enable him to see distant objects ; and had a being like 
ourselves made the atmosphere, he would have thought 
it enough to have created a medium so essential to 
animal life, that to live is to breathe, and to cease to 
breathe is to die. But beside this, the atmosphere has 
manifold uses, each entirely distinct from all the others. 
It conveys to plants, as well as animals, their nourish- 
ment and life ; it tempers the heat of Summer with its 
breezes; it binds down all fluids, and prevents their 
passing into the state of vapor ; it supports the clouds, 
distils the dew, and waters the earth with showers ; it 
multiplies the light of the sun, and diffuses it over earth 
and sky ; it feeds our fires, turns our machines, wafts 
our ships, and conveys to the ear all the sentiments of 
language, and all the melodies of music. 

In the third place, the wisdom of the Creator is strik- 
ingly manifested in the provision he has made for the 
stability of the universe. The perturbations occasioned 
by the motions of the planets, from their action on each 
other, are very numerous, since every body in the sys- 
tem exerts an attraction on every other, in conformity 
with the law of universal gravitation. Venus and Mer- 
cury, approaching, as they do at times, comparatively 
near to the earth, sensibly disturb its motions ; and the 
satellites of the remoter planets greatly disturb each 
other's movements. Nor was it possible to endow this 
principle with the properties it has, and make it operate 
as it does in regulating the motions of the world, with- 
out involving such an incident. On this subject, Pro- 
fessor Whewell, in his excellent work composing one of 


the Bridgewater Treatises, remarks : " The derangement 
which the planets produce in the motion of one of their 
number will be very small, in the course of one revolu- 
tion ; but this gives us no security that the derangement 
may not become very large, in the course of many rev- 
olutions. The cause acts perpetually, and it has the 
whole extent of time to work in. Is it not easily con- 
ceivable, then, that, in the lapse of ages, the derange- 
ments of the motions of the planets may accumulate, 
the orbits may change their form, and their mutual dis- 
tances may be much increased or diminished ? Is it 
not possible that these changes may go on without limit, 
and end in the complete subversion and ruin of the 
system ? If, for instance, the result of this mutual grav- 
itation should be to increase considerably the eccen- 
tricity of the earth's orbit, or to make the moon approach 
continually nearer and nearer to the earth, at every 
revolution, it is easy to see that, in the one case, our 
year would change its character, producing a far greater 
irregularity in the distribution of the solar heat ; in the 
other, our satellite must fall to the earth, occasioning a 
dreadful catastrophe. If the positions of the planetary 
orbits, with respect to that of the earth, were to change 
much, the planets might sometimes come very near us, 
and thus increase the effect of their attraction beyond 
calculable limits. Under such circumstances, c we might 
have years of unequal length, and seasons of capricious 
temperature ; planets and moons, of portentous size and 
aspect, glaring and disappearing at uncertain intervals ; 
tides, like deluges, sweeping over whole continents; 
and perhaps the collision of two of the planets, and the 
consequent destruction of all organization on both of 
them.' The fact really is, that changes are taking place 
in the motions of the heavenly bodies, which have gone 
on progressively, from the first dawn of science. The 
eccentricity of the earth's orbit has been diminishing 
from the earliest observations to our times. The moon 
has been moving quicker from the time of the first re- 
corded eclipses, and is now- in advance, by about four 


times her own breadth, of what her own place would 
have been, if it had not been affected by this accelera- 
tion. The obliquity of the ecliptic, also, is in a state 
of diminution, and is now about two fifths of a degree 
less than it was in the time of Aristotle." 

But amid so many seeming causes of irregularity and 
ruin, it is worthy of a grateful notice, that effectual pro- 
vision is made for the stability of the solar system. The 
full confirmation of this fact is among the grand results 
of physical astronomy. " Newton did not undertake to 
demonstrate either the stability or instability of the sys- 
tem. The decision of this point required a great num- 
ber of preparatory steps and simplifications, and such 
progress in the invention and improvement of mathe- 
matical methods, as occupied the best mathematicians 
of Europe for the greater part of the last century. Tow- 
ards the end of that time, it was shown by La Grange 
and La Place, that the arrangements of the solar sys- 
tem are stable ; that, in the long run, the orbits and 
motions remain unchanged ; and that the changes in 
the orbits, which take place in shorter periods, never 
transgress certain very moderate limits. Each orbit 
undergoes deviations on this side and on that side of 
its average state ; but these deviations are never very 
great, and it finally recovers from them, so that the 
average is preserved. The planets produce perpetual 
perturbations in each other's motions ; but these per- 
turbations are not indefinitely progressive, but periodi- 
cal, reaching a maximum value, and then diminishing. 
The periods which this restoration requires are, for the 
most part, enormous, not less than thousands, and in 
some instances, millions, of years. Indeed, some of 
these apparent derangements have been going on in the 
same direction from the creation of the world. But the 
restoration is in the sequel as complete as the derange- 
ment ; and in the mean time the disturbance never at- 
tains a sufficient amount seriously to affect the stability 
of the system. ' I have succeeded in demonstrating/ 
says La Place, * that, whatever be the masses of the 


planets, in consequence of the fact that they all move 
in the same direction, in orbits of small eccentricity, 
and but slightly inclined to each other, their secular ir- 
regularities are periodical, and included within narrow 
limits ; so that the planetary system will only oscillate 
about a mean state, and will never deviate from it, ex- 
cept by a very small quantity. The ellipses of the 
planets have been and always will be nearly circular. 
The ecliptic will never coincide with the equator ; and 
the entire extent of the variation, in its inclination, can- 
not exceed three degrees.' ' : 

To these observations of La Place, Professor Whewell 
adds the following, on the importance, to the stability 
of the solar system, of the fact that those planets which 
have great masses have orbits of small eccentricity. 
"The planets Mercury and Mars, which have much 
the largest eccentricity among the old planets, are 
those of which the masses are much the smallest. The 
mass of Jupiter is more than two thousand times that 
of either of these planets. If the orbit of Jupiter were 
as eccentric as that of Mercury, all the security for 
the stability of the system, which analysis has yet 
pointed out, would disappear. The earth and the 
smaller planets might, by the near approach of Jupiter 
at his perihelion, change their nearly circular orbits 
into very long ellipses, and thus might fall into the sun, 
or fly off into remoter space. It is further remarkable, 
that in the newly-discovered planets, of which the or- 
bits are still more eccentric than that of Mercury, the 
masses are still smaller, so that the same provision is 
established in this case, also." 

With this hasty glance at the unity, power, and wis- 
dom, of the Creator, as manifested in the greatest of 
His works, I close. I hope enough has been said to 
vindicate the sentiment that called ' Devotion, daughter 
of Astronomy !' I do not pretend that this, or any 
other science, is adequate of itself to purify the heart, or 
to raise it to its Maker ; but I fully believe that, when 
the heart is already under the power of religion, there 


is something in the frequent and habitual contemplation 
of the heavenly bodies under all the lights of modern 
astronomy, very favorable to devotional feelings, in- 
spiring, as it does, humility, in unison with an exalted 
sentiment of grateful adoration. 

I have thus, my dear Friend, responded to your call, 
in such a manner as I could, in the transient intervals 
between severer professional studies, and by appropri- 
ating to you nearly the whole of my long vacation. In 
giving publicity to these Letters, how happy should I 
be, to find that they prove acceptable and even attrac- 
tive to the youth of our country, of both sexes. The 
inquiry has often pressed itself upon me, when enjoy- 
ing myself so high a degree of pleasure from the stu- 
dy of both the science and the literature of astrono- 
my, Cannot the reading community, especially the 
youthful part of it, learn how much more solid and 
enduring pleasure is to be derived from truth than from 
fiction ? Sated as the present age has been with ficti- 
tious narratives, is it not ready for a change ? And 
if truth can be disrobed of her severity, and arrayed in 
a more attractive garb than she usually wears, is not 
this a favorable moment for bringing her forward from 
the obscurity into which she has long been forced by 
her powerful rival ? In the schools, indeed, where men- 
tal discipline is the leading object, science must be per- 
mitted to retain her wonted rigor ; but I see not why, 
for the purposes of the general reader, she may not re- 
lax her features, and be happily allied with her own lit- 
erature. That you, dear Madam, will use your influence 
to effect such a change of taste among your youthful 
friends, as may lead them to prefer the interesting and 
exalted truths of astronomy above the most enticing 
works of fiction, I cannot for a moment doubt. And 
in this expectation, I bid you, affectionately, 




Bellatrix, . ; V . 


Alamak, . 

. 371 

Betalgeus, ' * ; ,. 


Aldebaran, . 


Bissextile, . . . 


Alexandrian school, . 

. 394 

Bootes, . " .' ;' 


Algenib, <A " - 


Bouguer, . . .-,," 


Algol, . ':.,.> 

. 371 

Bowditch, . , : ,.;^ .-,, 


Alioth, . . fa 


Brahean system, 


Almagest, . ,. . 

. 14 

Altair, . P V\'Y 1 " 



Altitude, . .'. . .' 

. 20 

Caesar, Julius, . . , :. 


Amplitude, . s; 

; 20 

Calendar, Grecian, . , - r 


Anaxagoras, . . w ( 

. 395 

** Gregorian, , ' 


Anaximander, * 


Cancer, . , . . 



. 371 

Canis Major, 




Canis Minor, ..( 


Antinous, . 

. 373 

Capella, . 




Capricorn, . ./,.., 


Apsides, . 

. 188 

Cassiopeia, . . . ; 




Catalogues of the stars, . 



Central forces, . 


Archimedes, . -v 


Cepheus, w^ f - 


A returns, . V : ' ^ 

. 372 

Ceres, . ,*' : v,.-> < * -i >5. 


Aries, . 

,*', 369 

Cetus, .... 


Aristotle, . 

. 136 



Astrology, . v . 




Astronomers royal, 

48, 404 

Circles, great and small, . 


Astronomical clock, 


** of diurnal revolution 

, 81 

Astronomical tables, . 

. 190 

" of perpetual appa- 

Astronomy, . . 

'..."" 17 



" history of, 


** of perpetual occul- 


100, 410 





" vertical, . 



Clusters, . 


Axis of the Earth, . 

-w 21 

Colures, .* . 


Azimuth, . . * 

. 20 

Coma Berenices, . , . 


Comet, Biela's, . , . 



" Encke's, 



16, 136 

' Halley's, . ; { ^ 


Base line, 


Comets, .... 


Base of verification, . 

. 79 

' brightness of, . 




Comets, distances of, . 


Equations, periodical, 


light of, . 


" secular, 


magnitude of, 


" tabular, . 


mass of, . 




motions of, . 




number of, 


*' precession of the, 


periods of, . 


Eudoxus, .... 


perturbations of, 


structure of, . 



tails of, . 






Fraunhofer, . 


Conjunction, . 


Constellations, . 



Copernican system, 256, 


Galaxy, .... 


Copernicus, . . 14, 




Cor Caroli, 


" abjuration of, 


Cor Hydrae, 


" condemnation of, 


Corona Borealis, . 


" life of, . 


Corvus, .... 


** persecutions of, 




Gemini, .... 


Crystalline spheres, . 




Cygnus, . . ... . 


Globes, artificial, 



Gravitation, universal, . 



Gravity, terrestrial, . 


Day, astronomical, 


" sidereal, . 



.... 60 

Days of the week, . . 68 

Declination, ... 24 

Deferents, . . . 400 

Denebola, . . . 370 
Distances of the heavenly 

bodies, how measured, . 94 

Distances of the stars, . 387 

Dolphin, . . . .373 

Double stars, . . 381 

Draco, . . . .374 


Earth, diameter of the, 
" ellipticity of the, 
" figure of the, . 
" motion of the, 
" orbit of the, . 

Eclipses, annular, 
" calculation of, 

'* of the moon, . 
" of the sun, . 



Equation of time, . 

Hercules, .... 372 

Herschel, Sir Wm., 36, 105, 383 

Hesperus, . . . 397 

Hipparchus, . . . 398 

Horizon, rational, . . 20 

" sensible, . . 20 

Hour-circles, ... 21 

Huyghens, ... 72 


Inductive system, . . 137 

Inquisition, . . . 138 

Instruments, astronomical, 29 













belts of, 



diameter of, 



distance of, . 



eclipses of, 




magnitude of, 




satellites of, 




scenery of, . 




telescopic view of, 





Kepler, . . . .300 
Kepler's law, . . 296 

Latitude, .... 
" how found, 

Laws of motion, , "> {* 
" terrestrial gravity, 

Leap year, 

Leo, . . . .-*>jti 

Leo Minor, 

Libra, .... 

Librations of the moon, 

Light, velocity of, how 
measured, . . ,<& ... 

Longitude, celestial, '-r# : ''. 
its importance, 
how found, 
by chronometers, 
by eclipses, 
by Jupiter's sat- 
ellites, . -; -y 






" by lunar method, 213 

Lucifer, . . . .397 
Lynx, .... 372 


Magnitudes, how measured, 94 

Magellan clouds, . . 378 

Mars, 245 

" changes of, . . 245 

' distance of, . . 245 

" revolutions of, . . 246 

Mecanique Celeste, . 148 

Mercury, .... 230 

** conjunctions of, 231 

" diurnal revolution of, 235 

" phases of, . . 234 

" sidereal revolut'n of, 231 

" synodical " 231 

" transits of, . . 237 

Meridian, . '>'.'- -' 20 

Meteoric showers, . . 346 

" " origin of, 350 

Meteoric stones, . . 290 

Metonic cycle, . . 192 

Miletus, school of, . . 394 

Milky Way, ... 379 

Mira, . . e . . 375 

Mirach, . . . .371 

Mizar, . .'. '. . fe 374 

Month, sidereal, ' . - .173 

" synodical, . . 173 

Moon, . . . .157 

atmosphere of the, 167 

cusps of the, . . 174 

diameter of the, . 158 

distance of the, . 158 

eclipses of the, . 195 

harvest, . . . 177 

irregularities of the, 186 

librations of the, . 179 

light of the, . . 158 

mountains in the, . 159 

nodes of the, . 173 

phases of the, . . 174 
revolutions of the, 178-182 

scenery of the, . 163 
telescopic appear- 

ance of the, . . 158 

volcanoes in the, . 166 

volume of the, . 158 

Motion, laws of, . . 126 

Motions of the planets, . 291 

Mural circle, ' .-;- J''- 54 


Nadir, .... 20 

Nature of the stars, . 390 

Nebulte, . . . .377 

New planets, . . 286 

" distances of, , 288 

" origin of, . 289 

" periods of, . 288 

" size of, . 289 

New style, ... 66 


. 16,143 


Oblique sphere, . . 84 

Obliquity of the ecliptic, 115 

" effect of, on the 

Seasons, . .123 

" how found, . 117 
Observatory, ... 42 

" Greenwich, 42-48 

" Tycho's, . 42 

Old style, . ''-.>.' 66 
Ophiucus, . ,. . 872 

Opposition, . . . 200 



Orion, .... 


Regulus, .... 


Orreries, . . . 112, 


Resolution of motion, 





Revolution, annual, 


Pallas, .... 


diurnal, . 


Parallactic arc, 


Rigel, .... 


Parallax, . . .90, 


Right ascension, 


" annual, . 


Right sphere, 


'* horizontal, . 


" how found, 



Parallel sphere, . 




Parallels of latitude, 


Saros, .... 


Pegasus, .... 


Saturn, .... 




" diameter of, 


Perigee, .... 


" ring of, 


Periodical inequalities, . 


" satellites of, 


Perseus, . 


" scenery of, 


Pisces, .... 




Piscis Australis, 


Seasons, .... 






distances of, . 


Secular inequalities, . 


inferior, . 




magnitudes of, 


Sextant, .... 


periods, . 


Sidereal day, 




" month, 




Signs, .... 


Pointers, .... 


Sirius, .... 


Polar distance, 




Polaris, .... 


Sphere, celestial, 


Pole, .... 


" doctrine of the, . 


" of the earth, 


" oblique, 


Pollux, .... 


" parallel, . 


Power of the Deity, . 


" right, . 




" terrestrial, 




Spica, .... 


Prime vertical, 


Spots on the sun, . 


Primum mobile, 


" " cause of, 




" " dimensions of, 


Procyon, .... 


" " number of, . 


Projection of the sphere, 


Stability of the universe, 


Proper motions of the stars, 


Stars, fixed, 


Ptolemaic system, 


Stylus, .... 








e attraction of the, . 


* density of the, . 



* diameter of the, 




c distance of the, . 


* mass of the, . 



* nature and constitu- 

Radius, .... 


tion of the, 


Refraction, . 


" revolutions of the, . 




Sun, spots on the, 

. 104 


'* volume of the, 

,~ 103 

Unity of the Deity, . 

. 407 


. 18 



System of the world, 


diameter of, . 

. 283 

" Brahean, . 


distance of, 


'* Copernican, . 

. 401 

history of, 

. 284 

" Ptolemaic, 


period of, . 


satellites of, . 

. 284 


scenery of, .*,- 


Tangent, . 

. 129 

Ursa Major, 

. 373 



Ursa Minor, . 


Telescope, the, . 

. 31 




directions for using, 39 

Variable stars, . 

. 379 



Venus, .... 



, . 36 

conjunctions of, 

. 231 

history of 


mountains of, 



. 34 

phases of, 

. 234 

Temperature, changes 

of, 124 

revolutions of, 


Temporary stars, 

. 380 

transits of, 

. 239 

Terminator, . 

119, 159 

Vesta, .... 


Thales, . 



. 370 

Tides, . 

.< 216 

Virgo, . . . - ,. 


' cause of, . 

. 216 

' spring and neap, 




. 59 

Year, astronomical, . 

. 63 

* apparent, 


" tropical, 


' equation of, 

. 61 

* mean, 



* sidereal, . . 

. 60 





Zenith distance, 


Triangulation, . 

. 75 


. 26 



Zodiacal light, 


Twilight, . 

. 98 Zones, 

. 25 


Return to desk from which borrowed. 
This book is DUE on the last date stamped beloi 

s I 

FEB261967 9 


APR 2 8 1980 



LD 21-100m-ll,'49(B7146sl6)476